Solve 2x^4y-10=0 - ScanMath

Solve the equation

Solve for x

Solve for y

x = - \frac{4 5 y ^{3}}{∣ y ∣}, y \neq = 0 x = \frac{4 5 y ^{3}}{∣ y ∣}, y \neq = 0

Show Solution

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

r = 5 5 sec^{4} (θ) csc (θ)

Show Solution

Find the derivative with respect to x

Find the derivative with respect to y

\frac{d y}{d x} = - \frac{4 y}{x}

Show Solution

Find the second derivative with respect to x

Find the second derivative with respect to y

\frac{d ^{2} y}{d x ^{2}} = \frac{20 y}{x ^{2}}

Calculate

2 x^{4} y - 10 = 0

Take the derivative of both sides

\frac{d}{d x} (2 x^{4} y - 10) = \frac{d}{d x} (0)

Calculate the derivative

More Steps

8 x^{3} y + 2 x^{4} \frac{d y}{d x} = \frac{d}{d x} (0)

Calculate the derivative

8 x^{3} y + 2 x^{4} \frac{d y}{d x} = 0

Move the expression to the right-hand side and change its sign

2 x^{4} \frac{d y}{d x} = 0 - 8 x^{3} y

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

2 x^{4} \frac{d y}{d x} = - 8 x^{3} y

Divide both sides

\frac{2 x ^{4} \frac{d y}{d x}}{2 x ^{4}} = \frac{- 8 x ^{3} y}{2 x ^{4}}

Divide the numbers

\frac{d y}{d x} = \frac{- 8 x ^{3} y}{2 x ^{4}}

Divide the numbers

More Steps

\frac{d y}{d x} = - \frac{4 y}{x}

Take the derivative of both sides

\frac{d}{d x} (\frac{d y}{d x}) = \frac{d}{d x} (- \frac{4 y}{x})

Calculate the derivative

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

Use differentiation rules

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

Calculate the derivative

More Steps

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

Use \frac{d}{d x} x^{n} = n x^{n - 1} to find derivative

\frac{d ^{2} y}{d x ^{2}} = - \frac{4 \frac{d y}{d x} \times x - 4 y \times 1}{x ^{2}}

Use the commutative property to reorder the terms

\frac{d ^{2} y}{d x ^{2}} = - \frac{4 x \frac{d y}{d x} - 4 y \times 1}{x ^{2}}

Any expression multiplied by 1 remains the same

\frac{d ^{2} y}{d x ^{2}} = - \frac{4 x \frac{d y}{d x} - 4 y}{x ^{2}}

Use equation \frac{d y}{d x} = - \frac{4 y}{x} to substitute

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

Solution

More Steps

\frac{d ^{2} y}{d x ^{2}} = \frac{20 y}{x ^{2}}

Show Solution