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Popular >

derivative of \sqrt[5]{1/(y^2)}

Solution

derivative of

Solution

- \frac{2 ( y ^{2} ) ^{\frac{4}{5}}}{5 y ^{3}}

Solution steps

Apply the chain rule:

\frac{1}{5 ( \frac{1}{y ^{2}} ) ^{\frac{4}{5}}} \frac{d}{d y} (\frac{1}{y ^{2}})

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

\frac{d}{d y} (\frac{1}{y ^{2}}) = - \frac{2}{y ^{3}}

= \frac{1}{5 ( \frac{1}{y ^{2}} ) ^{\frac{4}{5}}} (- \frac{2}{y ^{3}})

Simplify

\frac{1}{5 ( \frac{1}{y ^{2}} ) ^{\frac{4}{5}}} (- \frac{2}{y ^{3}}) : - \frac{2 ( y ^{2} ) ^{\frac{4}{5}}}{5 y ^{3}}

= - \frac{2 ( y ^{2} ) ^{\frac{4}{5}}}{5 y ^{3}}

Popular Examples

derivative of f(x)=(4x-1)/(x+5)derivative of

f (x) = \frac{4 x - 1}{x + 5}

tangent of f(x)=(5x-x^2)(5-x-x^2)tangent of

f (x) = (5 x - x^{2}) (5 - x - x^{2})

(\partial)/(\partial t)(t^2x-t)

\frac{\partial}{\partial t} (t^{2} x - t)

integral of x/(sqrt(x^2+9))

\int \frac{x}{x ^{2} + 9} d x

laplacetransform 6t^3+5cos(2t)laplace transform

6 t^{3} + 5 cos (2 t)

Frequently Asked Questions (FAQ)

What is the derivative of \sqrt[5]{1/(y^2)} ?
The derivative of \sqrt[5]{1/(y^2)} is -(2(y^2)^{4/5})/(5y^3)
What is the first derivative of \sqrt[5]{1/(y^2)} ?
The first derivative of \sqrt[5]{1/(y^2)} is -(2(y^2)^{4/5})/(5y^3)