Solve (2x-5)/(x y) = 3-y

Question

Solve the equation

Solve for x

Solve for y

x = \frac{5}{2 - 3 y + y ^{2}}

Show Solution

Testing for symmetry

Testing for symmetry about the origin

Testing for symmetry about the x-axis

Testing for symmetry about the y-axis

Not symmetry with respect to the origin

Show Solution

Find the first derivative

Find the derivative with respect to x

Find the derivative with respect to y

\frac{d y}{d x} = \frac{5 y}{2 x ^{2} - 5 x - x ^{2} y ^{2}}

Calculate

\frac{2 x - 5}{x y} = 3 - y

Take the derivative of both sides

\frac{d}{d x} (\frac{2 x - 5}{x y}) = \frac{d}{d x} (3 - y)

Calculate the derivative

More Steps

\frac{- 2 x ^{2} \frac{d y}{d x} + 5 y + 5 x \frac{d y}{d x}}{x ^{2} y ^{2}} = \frac{d}{d x} (3 - y)

Calculate the derivative

More Steps

\frac{- 2 x ^{2} \frac{d y}{d x} + 5 y + 5 x \frac{d y}{d x}}{x ^{2} y ^{2}} = - \frac{d y}{d x}

Cross multiply

- 2 x^{2} \frac{d y}{d x} + 5 y + 5 x \frac{d y}{d x} = x^{2} y^{2} (- \frac{d y}{d x})

Simplify the equation

- 2 x^{2} \frac{d y}{d x} + 5 y + 5 x \frac{d y}{d x} = - x^{2} y^{2} \frac{d y}{d x}

Collect like terms by calculating the sum or difference of their coefficients

(- 2 x^{2} + 5 x) \frac{d y}{d x} + 5 y = - x^{2} y^{2} \frac{d y}{d x}

Move the variable to the left side

(- 2 x^{2} + 5 x) \frac{d y}{d x} + 5 y + x^{2} y^{2} \frac{d y}{d x} = 0

Collect like terms by calculating the sum or difference of their coefficients

(- 2 x^{2} + 5 x + x^{2} y^{2}) \frac{d y}{d x} + 5 y = 0

Move the constant to the right side

(- 2 x^{2} + 5 x + x^{2} y^{2}) \frac{d y}{d x} = 0 - 5 y

Removing 0 doesn't change the value,so remove it from the expression

(- 2 x^{2} + 5 x + x^{2} y^{2}) \frac{d y}{d x} = - 5 y

Divide both sides

\frac{( - 2 x ^{2} + 5 x + x ^{2} y ^{2} ) \frac{d y}{d x}}{- 2 x ^{2} + 5 x + x ^{2} y ^{2}} = \frac{- 5 y}{- 2 x ^{2} + 5 x + x ^{2} y ^{2}}

Divide the numbers

\frac{d y}{d x} = \frac{- 5 y}{- 2 x ^{2} + 5 x + x ^{2} y ^{2}}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

\frac{d y}{d x} = - \frac{5 y}{- 2 x ^{2} + 5 x + x ^{2} y ^{2}}

Solution

More Steps

\frac{d y}{d x} = \frac{5 y}{2 x ^{2} - 5 x - x ^{2} y ^{2}}

Show Solution

Find the second derivative

\frac{d ^{2} y}{d x ^{2}} = \frac{200 x y - 250 y - 50 y ^{3} x - 40 x ^{2} y + 40 x ^{2} y ^{3} - 10 x ^{2} y ^{5}}{8 x ^{5} + 150 x ^{3} + 6 x ^{5} y ^{4} - 60 x ^{4} - 12 x ^{5} y ^{2} + 60 x ^{4} y ^{2} - 125 x ^{2} - 15 x ^{4} y ^{4} - 75 x ^{3} y ^{2} - x ^{5} y ^{6}}

Calculate

\frac{2 x - 5}{x y} = 3 - y

Take the derivative of both sides

\frac{d}{d x} (\frac{2 x - 5}{x y}) = \frac{d}{d x} (3 - y)

Calculate the derivative

More Steps

\frac{- 2 x ^{2} \frac{d y}{d x} + 5 y + 5 x \frac{d y}{d x}}{x ^{2} y ^{2}} = \frac{d}{d x} (3 - y)

Calculate the derivative

More Steps

\frac{- 2 x ^{2} \frac{d y}{d x} + 5 y + 5 x \frac{d y}{d x}}{x ^{2} y ^{2}} = - \frac{d y}{d x}

Cross multiply

- 2 x^{2} \frac{d y}{d x} + 5 y + 5 x \frac{d y}{d x} = x^{2} y^{2} (- \frac{d y}{d x})

Simplify the equation

- 2 x^{2} \frac{d y}{d x} + 5 y + 5 x \frac{d y}{d x} = - x^{2} y^{2} \frac{d y}{d x}

Collect like terms by calculating the sum or difference of their coefficients

(- 2 x^{2} + 5 x) \frac{d y}{d x} + 5 y = - x^{2} y^{2} \frac{d y}{d x}

Move the variable to the left side

(- 2 x^{2} + 5 x) \frac{d y}{d x} + 5 y + x^{2} y^{2} \frac{d y}{d x} = 0

Collect like terms by calculating the sum or difference of their coefficients

(- 2 x^{2} + 5 x + x^{2} y^{2}) \frac{d y}{d x} + 5 y = 0

Move the constant to the right side

(- 2 x^{2} + 5 x + x^{2} y^{2}) \frac{d y}{d x} = 0 - 5 y

Removing 0 doesn't change the value,so remove it from the expression

(- 2 x^{2} + 5 x + x^{2} y^{2}) \frac{d y}{d x} = - 5 y

Divide both sides

\frac{( - 2 x ^{2} + 5 x + x ^{2} y ^{2} ) \frac{d y}{d x}}{- 2 x ^{2} + 5 x + x ^{2} y ^{2}} = \frac{- 5 y}{- 2 x ^{2} + 5 x + x ^{2} y ^{2}}

Divide the numbers

\frac{d y}{d x} = \frac{- 5 y}{- 2 x ^{2} + 5 x + x ^{2} y ^{2}}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

\frac{d y}{d x} = - \frac{5 y}{- 2 x ^{2} + 5 x + x ^{2} y ^{2}}

Simplify

More Steps

\frac{d y}{d x} = \frac{5 y}{2 x ^{2} - 5 x - x ^{2} y ^{2}}

Take the derivative of both sides

\frac{d}{d x} (\frac{d y}{d x}) = \frac{d}{d x} (\frac{5 y}{2 x ^{2} - 5 x - x ^{2} y ^{2}})

Calculate the derivative

\frac{d ^{2} y}{d x ^{2}} = \frac{d}{d x} (\frac{5 y}{2 x ^{2} - 5 x - x ^{2} y ^{2}})

Use differentiation rules

\frac{d ^{2} y}{d x ^{2}} = \frac{\frac{d}{d x} ( 5 y ) \times ( 2 x ^{2} - 5 x - x ^{2} y ^{2} ) - 5 y \times \frac{d}{d x} ( 2 x ^{2} - 5 x - x ^{2} y ^{2} )}{( 2 x ^{2} - 5 x - x ^{2} y ^{2} ) ^{2}}

Calculate the derivative

More Steps

\frac{d ^{2} y}{d x ^{2}} = \frac{5 \frac{d y}{d x} \times ( 2 x ^{2} - 5 x - x ^{2} y ^{2} ) - 5 y \times \frac{d}{d x} ( 2 x ^{2} - 5 x - x ^{2} y ^{2} )}{( 2 x ^{2} - 5 x - x ^{2} y ^{2} ) ^{2}}

Calculate the derivative

More Steps

\frac{d ^{2} y}{d x ^{2}} = \frac{5 \frac{d y}{d x} \times ( 2 x ^{2} - 5 x - x ^{2} y ^{2} ) - 5 y ( 4 x - 5 - 2 x y ^{2} - 2 x ^{2} y \frac{d y}{d x} )}{( 2 x ^{2} - 5 x - x ^{2} y ^{2} ) ^{2}}

Calculate

More Steps

\frac{d ^{2} y}{d x ^{2}} = \frac{10 x ^{2} \frac{d y}{d x} - 25 x \frac{d y}{d x} - 5 x ^{2} y ^{2} \frac{d y}{d x} - 5 y ( 4 x - 5 - 2 x y ^{2} - 2 x ^{2} y \frac{d y}{d x} )}{( 2 x ^{2} - 5 x - x ^{2} y ^{2} ) ^{2}}

Calculate

More Steps

\frac{d ^{2} y}{d x ^{2}} = \frac{10 x ^{2} \frac{d y}{d x} - 25 x \frac{d y}{d x} - 5 x ^{2} y ^{2} \frac{d y}{d x} - ( 20 y x - 25 y - 10 y ^{3} x - 10 y ^{2} x ^{2} \frac{d y}{d x} )}{( 2 x ^{2} - 5 x - x ^{2} y ^{2} ) ^{2}}

Calculate

More Steps

\frac{d ^{2} y}{d x ^{2}} = \frac{10 x ^{2} \frac{d y}{d x} - 25 x \frac{d y}{d x} + 5 x ^{2} y ^{2} \frac{d y}{d x} - 20 y x + 25 y + 10 y ^{3} x}{( 2 x ^{2} - 5 x - x ^{2} y ^{2} ) ^{2}}

Use equation \frac{d y}{d x} = \frac{5 y}{2 x ^{2} - 5 x - x ^{2} y ^{2}} to substitute

\frac{d ^{2} y}{d x ^{2}} = \frac{10 x ^{2} \times \frac{5 y}{2 x ^{2} - 5 x - x ^{2} y ^{2}} - 25 x \times \frac{5 y}{2 x ^{2} - 5 x - x ^{2} y ^{2}} + 5 x ^{2} y ^{2} \times \frac{5 y}{2 x ^{2} - 5 x - x ^{2} y ^{2}} - 20 y x + 25 y + 10 y ^{3} x}{( 2 x ^{2} - 5 x - x ^{2} y ^{2} ) ^{2}}

Solution

More Steps

Calculate

\frac{10 x ^{2} \times \frac{5 y}{2 x ^{2} - 5 x - x ^{2} y ^{2}} - 25 x \times \frac{5 y}{2 x ^{2} - 5 x - x ^{2} y ^{2}} + 5 x ^{2} y ^{2} \times \frac{5 y}{2 x ^{2} - 5 x - x ^{2} y ^{2}} - 20 y x + 25 y + 10 y ^{3} x}{( 2 x ^{2} - 5 x - x ^{2} y ^{2} ) ^{2}}

Multiply the terms

More Steps

\frac{\frac{50 x y}{2 x - 5 - x y ^{2}} - 25 x \times \frac{5 y}{2 x ^{2} - 5 x - x ^{2} y ^{2}} + 5 x ^{2} y ^{2} \times \frac{5 y}{2 x ^{2} - 5 x - x ^{2} y ^{2}} - 20 y x + 25 y + 10 y ^{3} x}{( 2 x ^{2} - 5 x - x ^{2} y ^{2} ) ^{2}}

Multiply the terms

\frac{\frac{50 x y}{2 x - 5 - x y ^{2}} - \frac{125 y}{2 x - 5 - x y ^{2}} + 5 x ^{2} y ^{2} \times \frac{5 y}{2 x ^{2} - 5 x - x ^{2} y ^{2}} - 20 y x + 25 y + 10 y ^{3} x}{( 2 x ^{2} - 5 x - x ^{2} y ^{2} ) ^{2}}

Multiply the terms

More Steps

\frac{\frac{50 x y}{2 x - 5 - x y ^{2}} - \frac{125 y}{2 x - 5 - x y ^{2}} + \frac{25 x y ^{3}}{2 x - 5 - x y ^{2}} - 20 y x + 25 y + 10 y ^{3} x}{( 2 x ^{2} - 5 x - x ^{2} y ^{2} ) ^{2}}

Calculate the sum or difference

More Steps

\frac{\frac{200 x y - 250 y - 50 y ^{3} x - 40 x ^{2} y + 40 x ^{2} y ^{3} - 10 x ^{2} y ^{5}}{2 x - 5 - x y ^{2}}}{( 2 x ^{2} - 5 x - x ^{2} y ^{2} ) ^{2}}

Multiply by the reciprocal

\frac{200 x y - 250 y - 50 y ^{3} x - 40 x ^{2} y + 40 x ^{2} y ^{3} - 10 x ^{2} y ^{5}}{2 x - 5 - x y ^{2}} \times \frac{1}{( 2 x ^{2} - 5 x - x ^{2} y ^{2} ) ^{2}}

Multiply the terms

\frac{200 x y - 250 y - 50 y ^{3} x - 40 x ^{2} y + 40 x ^{2} y ^{3} - 10 x ^{2} y ^{5}}{( 2 x - 5 - x y ^{2} ) ( 2 x ^{2} - 5 x - x ^{2} y ^{2} ) ^{2}}

Expand the expression

More Steps

Evaluate

(2 x - 5 - x y^{2}) (2 x^{2} - 5 x - x^{2} y^{2})^{2}

Evaluate the power

(2 x - 5 - x y^{2}) (4 x^{4} + 25 x^{2} + x^{4} y^{4} - 20 x^{3} - 4 x^{4} y^{2} + 10 x^{3} y^{2})

Apply the distributive property

2 x \times 4 x^{4} + 2 x \times 25 x^{2} + 2 x \times x^{4} y^{4} - 2 x \times 20 x^{3} - 2 x \times 4 x^{4} y^{2} + 2 x \times 10 x^{3} y^{2} - 5 \times 4 x^{4} - 5 \times 25 x^{2} - 5 x^{4} y^{4} - (- 5 \times 20 x^{3}) - (- 5 \times 4 x^{4} y^{2}) - 5 \times 10 x^{3} y^{2} - x y^{2} \times 4 x^{4} - x y^{2} \times 25 x^{2} - x y^{2} x^{4} y^{4} - (- x y^{2} \times 20 x^{3}) - (- x y^{2} \times 4 x^{4} y^{2}) - x y^{2} \times 10 x^{3} y^{2}

Multiply the terms

8 x^{5} + 2 x \times 25 x^{2} + 2 x \times x^{4} y^{4} - 2 x \times 20 x^{3} - 2 x \times 4 x^{4} y^{2} + 2 x \times 10 x^{3} y^{2} - 5 \times 4 x^{4} - 5 \times 25 x^{2} - 5 x^{4} y^{4} - (- 5 \times 20 x^{3}) - (- 5 \times 4 x^{4} y^{2}) - 5 \times 10 x^{3} y^{2} - x y^{2} \times 4 x^{4} - x y^{2} \times 25 x^{2} - x y^{2} x^{4} y^{4} - (- x y^{2} \times 20 x^{3}) - (- x y^{2} \times 4 x^{4} y^{2}) - x y^{2} \times 10 x^{3} y^{2}

Multiply the terms

8 x^{5} + 50 x^{3} + 2 x \times x^{4} y^{4} - 2 x \times 20 x^{3} - 2 x \times 4 x^{4} y^{2} + 2 x \times 10 x^{3} y^{2} - 5 \times 4 x^{4} - 5 \times 25 x^{2} - 5 x^{4} y^{4} - (- 5 \times 20 x^{3}) - (- 5 \times 4 x^{4} y^{2}) - 5 \times 10 x^{3} y^{2} - x y^{2} \times 4 x^{4} - x y^{2} \times 25 x^{2} - x y^{2} x^{4} y^{4} - (- x y^{2} \times 20 x^{3}) - (- x y^{2} \times 4 x^{4} y^{2}) - x y^{2} \times 10 x^{3} y^{2}

Multiply the terms

8 x^{5} + 50 x^{3} + 2 x^{5} y^{4} - 2 x \times 20 x^{3} - 2 x \times 4 x^{4} y^{2} + 2 x \times 10 x^{3} y^{2} - 5 \times 4 x^{4} - 5 \times 25 x^{2} - 5 x^{4} y^{4} - (- 5 \times 20 x^{3}) - (- 5 \times 4 x^{4} y^{2}) - 5 \times 10 x^{3} y^{2} - x y^{2} \times 4 x^{4} - x y^{2} \times 25 x^{2} - x y^{2} x^{4} y^{4} - (- x y^{2} \times 20 x^{3}) - (- x y^{2} \times 4 x^{4} y^{2}) - x y^{2} \times 10 x^{3} y^{2}

Multiply the terms

8 x^{5} + 50 x^{3} + 2 x^{5} y^{4} - 40 x^{4} - 2 x \times 4 x^{4} y^{2} + 2 x \times 10 x^{3} y^{2} - 5 \times 4 x^{4} - 5 \times 25 x^{2} - 5 x^{4} y^{4} - (- 5 \times 20 x^{3}) - (- 5 \times 4 x^{4} y^{2}) - 5 \times 10 x^{3} y^{2} - x y^{2} \times 4 x^{4} - x y^{2} \times 25 x^{2} - x y^{2} x^{4} y^{4} - (- x y^{2} \times 20 x^{3}) - (- x y^{2} \times 4 x^{4} y^{2}) - x y^{2} \times 10 x^{3} y^{2}

Multiply the terms

8 x^{5} + 50 x^{3} + 2 x^{5} y^{4} - 40 x^{4} - 8 x^{5} y^{2} + 2 x \times 10 x^{3} y^{2} - 5 \times 4 x^{4} - 5 \times 25 x^{2} - 5 x^{4} y^{4} - (- 5 \times 20 x^{3}) - (- 5 \times 4 x^{4} y^{2}) - 5 \times 10 x^{3} y^{2} - x y^{2} \times 4 x^{4} - x y^{2} \times 25 x^{2} - x y^{2} x^{4} y^{4} - (- x y^{2} \times 20 x^{3}) - (- x y^{2} \times 4 x^{4} y^{2}) - x y^{2} \times 10 x^{3} y^{2}

Multiply the terms

8 x^{5} + 50 x^{3} + 2 x^{5} y^{4} - 40 x^{4} - 8 x^{5} y^{2} + 20 x^{4} y^{2} - 5 \times 4 x^{4} - 5 \times 25 x^{2} - 5 x^{4} y^{4} - (- 5 \times 20 x^{3}) - (- 5 \times 4 x^{4} y^{2}) - 5 \times 10 x^{3} y^{2} - x y^{2} \times 4 x^{4} - x y^{2} \times 25 x^{2} - x y^{2} x^{4} y^{4} - (- x y^{2} \times 20 x^{3}) - (- x y^{2} \times 4 x^{4} y^{2}) - x y^{2} \times 10 x^{3} y^{2}

Multiply the numbers

8 x^{5} + 50 x^{3} + 2 x^{5} y^{4} - 40 x^{4} - 8 x^{5} y^{2} + 20 x^{4} y^{2} - 20 x^{4} - 5 \times 25 x^{2} - 5 x^{4} y^{4} - (- 5 \times 20 x^{3}) - (- 5 \times 4 x^{4} y^{2}) - 5 \times 10 x^{3} y^{2} - x y^{2} \times 4 x^{4} - x y^{2} \times 25 x^{2} - x y^{2} x^{4} y^{4} - (- x y^{2} \times 20 x^{3}) - (- x y^{2} \times 4 x^{4} y^{2}) - x y^{2} \times 10 x^{3} y^{2}

Multiply the numbers

8 x^{5} + 50 x^{3} + 2 x^{5} y^{4} - 40 x^{4} - 8 x^{5} y^{2} + 20 x^{4} y^{2} - 20 x^{4} - 125 x^{2} - 5 x^{4} y^{4} - (- 5 \times 20 x^{3}) - (- 5 \times 4 x^{4} y^{2}) - 5 \times 10 x^{3} y^{2} - x y^{2} \times 4 x^{4} - x y^{2} \times 25 x^{2} - x y^{2} x^{4} y^{4} - (- x y^{2} \times 20 x^{3}) - (- x y^{2} \times 4 x^{4} y^{2}) - x y^{2} \times 10 x^{3} y^{2}

Multiply the numbers

8 x^{5} + 50 x^{3} + 2 x^{5} y^{4} - 40 x^{4} - 8 x^{5} y^{2} + 20 x^{4} y^{2} - 20 x^{4} - 125 x^{2} - 5 x^{4} y^{4} - (- 100 x^{3}) - (- 5 \times 4 x^{4} y^{2}) - 5 \times 10 x^{3} y^{2} - x y^{2} \times 4 x^{4} - x y^{2} \times 25 x^{2} - x y^{2} x^{4} y^{4} - (- x y^{2} \times 20 x^{3}) - (- x y^{2} \times 4 x^{4} y^{2}) - x y^{2} \times 10 x^{3} y^{2}

Multiply the numbers

8 x^{5} + 50 x^{3} + 2 x^{5} y^{4} - 40 x^{4} - 8 x^{5} y^{2} + 20 x^{4} y^{2} - 20 x^{4} - 125 x^{2} - 5 x^{4} y^{4} - (- 100 x^{3}) - (- 20 x^{4} y^{2}) - 5 \times 10 x^{3} y^{2} - x y^{2} \times 4 x^{4} - x y^{2} \times 25 x^{2} - x y^{2} x^{4} y^{4} - (- x y^{2} \times 20 x^{3}) - (- x y^{2} \times 4 x^{4} y^{2}) - x y^{2} \times 10 x^{3} y^{2}

Multiply the numbers

8 x^{5} + 50 x^{3} + 2 x^{5} y^{4} - 40 x^{4} - 8 x^{5} y^{2} + 20 x^{4} y^{2} - 20 x^{4} - 125 x^{2} - 5 x^{4} y^{4} - (- 100 x^{3}) - (- 20 x^{4} y^{2}) - 50 x^{3} y^{2} - x y^{2} \times 4 x^{4} - x y^{2} \times 25 x^{2} - x y^{2} x^{4} y^{4} - (- x y^{2} \times 20 x^{3}) - (- x y^{2} \times 4 x^{4} y^{2}) - x y^{2} \times 10 x^{3} y^{2}

Multiply the terms

8 x^{5} + 50 x^{3} + 2 x^{5} y^{4} - 40 x^{4} - 8 x^{5} y^{2} + 20 x^{4} y^{2} - 20 x^{4} - 125 x^{2} - 5 x^{4} y^{4} - (- 100 x^{3}) - (- 20 x^{4} y^{2}) - 50 x^{3} y^{2} - 4 x^{5} y^{2} - x y^{2} \times 25 x^{2} - x y^{2} x^{4} y^{4} - (- x y^{2} \times 20 x^{3}) - (- x y^{2} \times 4 x^{4} y^{2}) - x y^{2} \times 10 x^{3} y^{2}

Multiply the terms

8 x^{5} + 50 x^{3} + 2 x^{5} y^{4} - 40 x^{4} - 8 x^{5} y^{2} + 20 x^{4} y^{2} - 20 x^{4} - 125 x^{2} - 5 x^{4} y^{4} - (- 100 x^{3}) - (- 20 x^{4} y^{2}) - 50 x^{3} y^{2} - 4 x^{5} y^{2} - 25 x^{3} y^{2} - x y^{2} x^{4} y^{4} - (- x y^{2} \times 20 x^{3}) - (- x y^{2} \times 4 x^{4} y^{2}) - x y^{2} \times 10 x^{3} y^{2}

Multiply the terms

8 x^{5} + 50 x^{3} + 2 x^{5} y^{4} - 40 x^{4} - 8 x^{5} y^{2} + 20 x^{4} y^{2} - 20 x^{4} - 125 x^{2} - 5 x^{4} y^{4} - (- 100 x^{3}) - (- 20 x^{4} y^{2}) - 50 x^{3} y^{2} - 4 x^{5} y^{2} - 25 x^{3} y^{2} - x^{5} y^{6} - (- x y^{2} \times 20 x^{3}) - (- x y^{2} \times 4 x^{4} y^{2}) - x y^{2} \times 10 x^{3} y^{2}

Multiply the terms

8 x^{5} + 50 x^{3} + 2 x^{5} y^{4} - 40 x^{4} - 8 x^{5} y^{2} + 20 x^{4} y^{2} - 20 x^{4} - 125 x^{2} - 5 x^{4} y^{4} - (- 100 x^{3}) - (- 20 x^{4} y^{2}) - 50 x^{3} y^{2} - 4 x^{5} y^{2} - 25 x^{3} y^{2} - x^{5} y^{6} - (- 20 x^{4} y^{2}) - (- x y^{2} \times 4 x^{4} y^{2}) - x y^{2} \times 10 x^{3} y^{2}

Multiply the terms

8 x^{5} + 50 x^{3} + 2 x^{5} y^{4} - 40 x^{4} - 8 x^{5} y^{2} + 20 x^{4} y^{2} - 20 x^{4} - 125 x^{2} - 5 x^{4} y^{4} - (- 100 x^{3}) - (- 20 x^{4} y^{2}) - 50 x^{3} y^{2} - 4 x^{5} y^{2} - 25 x^{3} y^{2} - x^{5} y^{6} - (- 20 x^{4} y^{2}) - (- 4 x^{5} y^{4}) - x y^{2} \times 10 x^{3} y^{2}

Multiply the terms

8 x^{5} + 50 x^{3} + 2 x^{5} y^{4} - 40 x^{4} - 8 x^{5} y^{2} + 20 x^{4} y^{2} - 20 x^{4} - 125 x^{2} - 5 x^{4} y^{4} - (- 100 x^{3}) - (- 20 x^{4} y^{2}) - 50 x^{3} y^{2} - 4 x^{5} y^{2} - 25 x^{3} y^{2} - x^{5} y^{6} - (- 20 x^{4} y^{2}) - (- 4 x^{5} y^{4}) - 10 x^{4} y^{4}

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

8 x^{5} + 50 x^{3} + 2 x^{5} y^{4} - 40 x^{4} - 8 x^{5} y^{2} + 20 x^{4} y^{2} - 20 x^{4} - 125 x^{2} - 5 x^{4} y^{4} + 100 x^{3} + 20 x^{4} y^{2} - 50 x^{3} y^{2} - 4 x^{5} y^{2} - 25 x^{3} y^{2} - x^{5} y^{6} + 20 x^{4} y^{2} + 4 x^{5} y^{4} - 10 x^{4} y^{4}

Add the terms

8 x^{5} + 150 x^{3} + 2 x^{5} y^{4} - 40 x^{4} - 8 x^{5} y^{2} + 20 x^{4} y^{2} - 20 x^{4} - 125 x^{2} - 5 x^{4} y^{4} + 20 x^{4} y^{2} - 50 x^{3} y^{2} - 4 x^{5} y^{2} - 25 x^{3} y^{2} - x^{5} y^{6} + 20 x^{4} y^{2} + 4 x^{5} y^{4} - 10 x^{4} y^{4}

Add the terms

8 x^{5} + 150 x^{3} + 6 x^{5} y^{4} - 40 x^{4} - 8 x^{5} y^{2} + 20 x^{4} y^{2} - 20 x^{4} - 125 x^{2} - 5 x^{4} y^{4} + 20 x^{4} y^{2} - 50 x^{3} y^{2} - 4 x^{5} y^{2} - 25 x^{3} y^{2} - x^{5} y^{6} + 20 x^{4} y^{2} - 10 x^{4} y^{4}

Subtract the terms

8 x^{5} + 150 x^{3} + 6 x^{5} y^{4} - 60 x^{4} - 8 x^{5} y^{2} + 20 x^{4} y^{2} - 125 x^{2} - 5 x^{4} y^{4} + 20 x^{4} y^{2} - 50 x^{3} y^{2} - 4 x^{5} y^{2} - 25 x^{3} y^{2} - x^{5} y^{6} + 20 x^{4} y^{2} - 10 x^{4} y^{4}

Subtract the terms

8 x^{5} + 150 x^{3} + 6 x^{5} y^{4} - 60 x^{4} - 12 x^{5} y^{2} + 20 x^{4} y^{2} - 125 x^{2} - 5 x^{4} y^{4} + 20 x^{4} y^{2} - 50 x^{3} y^{2} - 25 x^{3} y^{2} - x^{5} y^{6} + 20 x^{4} y^{2} - 10 x^{4} y^{4}

Add the terms

8 x^{5} + 150 x^{3} + 6 x^{5} y^{4} - 60 x^{4} - 12 x^{5} y^{2} + 60 x^{4} y^{2} - 125 x^{2} - 5 x^{4} y^{4} - 50 x^{3} y^{2} - 25 x^{3} y^{2} - x^{5} y^{6} - 10 x^{4} y^{4}

Subtract the terms

8 x^{5} + 150 x^{3} + 6 x^{5} y^{4} - 60 x^{4} - 12 x^{5} y^{2} + 60 x^{4} y^{2} - 125 x^{2} - 15 x^{4} y^{4} - 50 x^{3} y^{2} - 25 x^{3} y^{2} - x^{5} y^{6}

Subtract the terms

8 x^{5} + 150 x^{3} + 6 x^{5} y^{4} - 60 x^{4} - 12 x^{5} y^{2} + 60 x^{4} y^{2} - 125 x^{2} - 15 x^{4} y^{4} - 75 x^{3} y^{2} - x^{5} y^{6}

\frac{200 x y - 250 y - 50 y ^{3} x - 40 x ^{2} y + 40 x ^{2} y ^{3} - 10 x ^{2} y ^{5}}{8 x ^{5} + 150 x ^{3} + 6 x ^{5} y ^{4} - 60 x ^{4} - 12 x ^{5} y ^{2} + 60 x ^{4} y ^{2} - 125 x ^{2} - 15 x ^{4} y ^{4} - 75 x ^{3} y ^{2} - x ^{5} y ^{6}}

\frac{d ^{2} y}{d x ^{2}} = \frac{200 x y - 250 y - 50 y ^{3} x - 40 x ^{2} y + 40 x ^{2} y ^{3} - 10 x ^{2} y ^{5}}{8 x ^{5} + 150 x ^{3} + 6 x ^{5} y ^{4} - 60 x ^{4} - 12 x ^{5} y ^{2} + 60 x ^{4} y ^{2} - 125 x ^{2} - 15 x ^{4} y ^{4} - 75 x ^{3} y ^{2} - x ^{5} y ^{6}}

Show Solution