Solve 9x^51y=94 - ScanMath

Solve the equation

Solve for x

Solve for y

x = \frac{5 2538 y ^{4}}{3 y}

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Testing for symmetry about the origin

Testing for symmetry about the x-axis

Testing for symmetry about the y-axis

Symmetry with respect to the origin

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r = \frac{6 94}{6 9 cos ^{5} ( θ ) sin ( θ )} r = - \frac{6 94}{6 9 cos ^{5} ( θ ) sin ( θ )}

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Find the derivative with respect to x

Find the derivative with respect to y

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

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Find the second derivative with respect to x

Find the second derivative with respect to y

\frac{d ^{2} y}{d x ^{2}} = \frac{30 y}{x ^{2}}

Calculate

9 x^{5} 1 y = 94

Simplify the expression

9 x^{5} y = 94

Take the derivative of both sides

\frac{d}{d x} (9 x^{5} y) = \frac{d}{d x} (94)

Calculate the derivative

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45 x^{4} y + 9 x^{5} \frac{d y}{d x} = \frac{d}{d x} (94)

Calculate the derivative

45 x^{4} y + 9 x^{5} \frac{d y}{d x} = 0

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

9 x^{5} \frac{d y}{d x} = 0 - 45 x^{4} y

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

9 x^{5} \frac{d y}{d x} = - 45 x^{4} y

Divide both sides

\frac{9 x ^{5} \frac{d y}{d x}}{9 x ^{5}} = \frac{- 45 x ^{4} y}{9 x ^{5}}

Divide the numbers

\frac{d y}{d x} = \frac{- 45 x ^{4} y}{9 x ^{5}}

Divide the numbers

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

Take the derivative of both sides

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

Calculate the derivative

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

Use differentiation rules

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

Calculate the derivative

More Steps

\frac{d ^{2} y}{d x ^{2}} = - \frac{5 \frac{d y}{d x} \times x - 5 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{5 \frac{d y}{d x} \times x - 5 y \times 1}{x ^{2}}

Use the commutative property to reorder the terms

\frac{d ^{2} y}{d x ^{2}} = - \frac{5 x \frac{d y}{d x} - 5 y \times 1}{x ^{2}}

Any expression multiplied by 1 remains the same

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

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

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

Solution

More Steps

\frac{d ^{2} y}{d x ^{2}} = \frac{30 y}{x ^{2}}

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