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Popular >

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

Solution

Solution

- \frac{2}{5 x ^{\frac{7}{5}}}

Solution steps

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= \frac{d}{d x} ((x^{2})^{- \frac{1}{5}})

Apply the chain rule:

- \frac{1}{5 ( x ^{2} ) ^{\frac{6}{5}}} \frac{d}{d x} (x^{2})

= - \frac{1}{5 ( x ^{2} ) ^{\frac{6}{5}}} \frac{d}{d x} (x^{2})

\frac{d}{d x} (x^{2}) = 2 x

= - \frac{1}{5 ( x ^{2} ) ^{\frac{6}{5}}} \cdot 2 x

Simplify

- \frac{1}{5 ( x ^{2} ) ^{\frac{6}{5}}} \cdot 2 x : - \frac{2}{5 x ^{\frac{7}{5}}}

= - \frac{2}{5 x ^{\frac{7}{5}}}

Popular Examples

laplacetransform {cos(t)}laplace transform

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f (t) = cos (8 t)

derivative of f(x)=x^3-3x+4 derivative of

f (x) = x^{3} - 3 x + 4

y^{''}+6y^'+5y=2x

y^{^{''}} + 6 y^{^{'}} + 5 y = 2 x

tangent of f(x)=3x^{1/2}+x^{3/2},\at x=16 tangent of

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Frequently Asked Questions (FAQ)

What is the derivative of 1/(\sqrt[5]{x^2}) ?
The derivative of 1/(\sqrt[5]{x^2}) is -2/(5x^{7/5)}
What is the first derivative of 1/(\sqrt[5]{x^2}) ?
The first derivative of 1/(\sqrt[5]{x^2}) is -2/(5x^{7/5)}