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Popular >

derivative of (0.25/(\sqrt[5]{x^2)})

Solution

Solution

- \frac{0.1}{x ^{\frac{7}{5}}}

Solution steps

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

Apply exponent rule:

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

= 0.25 \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

= 0.25 (- \frac{1}{5 ( x ^{2} ) ^{\frac{6}{5}}} \cdot 2 x)

Simplify

0.25 (- \frac{1}{5 ( x ^{2} ) ^{\frac{6}{5}}} \cdot 2 x) : - \frac{0.1}{x ^{\frac{7}{5}}}

= - \frac{0.1}{x ^{\frac{7}{5}}}

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Frequently Asked Questions (FAQ)

What is the derivative of (0.25/(\sqrt[5]{x^2)}) ?
The derivative of (0.25/(\sqrt[5]{x^2)}) is -(0.1)/(x^{7/5)}
What is the first derivative of (0.25/(\sqrt[5]{x^2)}) ?
The first derivative of (0.25/(\sqrt[5]{x^2)}) is -(0.1)/(x^{7/5)}