Solve y^5-13x=7 - ScanMath

Solve the equation

Solve for x

Solve for y

x = \frac{- 7 + y ^{5}}{13}

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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

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Find the derivative with respect to x

Find the derivative with respect to y

\frac{d y}{d x} = \frac{13}{5 y ^{4}}

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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{676}{25 y ^{9}}

Calculate

y^{5} - 13 x = 7

Take the derivative of both sides

\frac{d}{d x} (y^{5} - 13 x) = \frac{d}{d x} (7)

Calculate the derivative

More Steps

5 y^{4} \frac{d y}{d x} - 13 = \frac{d}{d x} (7)

Calculate the derivative

5 y^{4} \frac{d y}{d x} - 13 = 0

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

5 y^{4} \frac{d y}{d x} = 0 + 13

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

5 y^{4} \frac{d y}{d x} = 13

Divide both sides

\frac{5 y ^{4} \frac{d y}{d x}}{5 y ^{4}} = \frac{13}{5 y ^{4}}

Divide the numbers

\frac{d y}{d x} = \frac{13}{5 y ^{4}}

Take the derivative of both sides

\frac{d}{d x} (\frac{d y}{d x}) = \frac{d}{d x} (\frac{13}{5 y ^{4}})

Calculate the derivative

\frac{d ^{2} y}{d x ^{2}} = \frac{d}{d x} (\frac{13}{5 y ^{4}})

Use differentiation rules

\frac{d ^{2} y}{d x ^{2}} = \frac{13}{5} \times \frac{d}{d x} (\frac{1}{y ^{4}})

Rewrite the expression in exponential form

\frac{d ^{2} y}{d x ^{2}} = \frac{13}{5} \times \frac{d}{d x} (y^{- 4})

Calculate the derivative

More Steps

\frac{d ^{2} y}{d x ^{2}} = \frac{13}{5} (- 4 y^{- 5} \frac{d y}{d x})

Rewrite the expression

\frac{d ^{2} y}{d x ^{2}} = \frac{13}{5} (- \frac{4 \frac{d y}{d x}}{y ^{5}})

Calculate

\frac{d ^{2} y}{d x ^{2}} = - \frac{52 \frac{d y}{d x}}{5 y ^{5}}

Use equation \frac{d y}{d x} = \frac{13}{5 y ^{4}} to substitute

\frac{d ^{2} y}{d x ^{2}} = - \frac{52 \times \frac{13}{5 y ^{4}}}{5 y ^{5}}

Solution

More Steps

\frac{d ^{2} y}{d x ^{2}} = - \frac{676}{25 y ^{9}}

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