What is (\partial)/(\partial x)(1/(\sqrt[5]{x^4)}) ?

The answer to (\partial)/(\partial x)(1/(\sqrt[5]{x^4)}) is -4/(5x^{9/5)}

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(\partial)/(\partial x)(1/(\sqrt[5]{x^4)})

- \frac{4}{5 x ^{\frac{9}{5}}}

Solution steps

Apply exponent rule:

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

= \frac{\partial}{\partial x} ((x^{4})^{- \frac{1}{5}})

Apply the chain rule:

- \frac{1}{5 ( x ^{4} ) ^{\frac{6}{5}}} \frac{\partial}{\partial x} (x^{4})

= - \frac{1}{5 ( x ^{4} ) ^{\frac{6}{5}}} \frac{\partial}{\partial x} (x^{4})

\frac{\partial}{\partial x} (x^{4}) = 4 x^{3}

= - \frac{1}{5 ( x ^{4} ) ^{\frac{6}{5}}} \cdot 4 x^{3}

Simplify

- \frac{1}{5 ( x ^{4} ) ^{\frac{6}{5}}} \cdot 4 x^{3} : - \frac{4}{5 x ^{\frac{9}{5}}}

= - \frac{4}{5 x ^{\frac{9}{5}}}

\frac{4}{( s + 2 ) ^{3}}

x \to 0 lim ((3 x + 1))

f (x) = lo g_{10} (x)

\int \frac{x ^{2} + 2 x + 4}{( x + 1 ) ^{3}} d x

\int 5 tan^{2} (x) d x

What is (\partial)/(\partial x)(1/(\sqrt[5]{x^4)}) ?
The answer to (\partial)/(\partial x)(1/(\sqrt[5]{x^4)}) is -4/(5x^{9/5)}