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

The derivative of 1/(\sqrt[4]{x^5}) is -5/(4x^{9/4)}

What is the first derivative of 1/(\sqrt[4]{x^5}) ?

The first derivative of 1/(\sqrt[4]{x^5}) is -5/(4x^{9/4)}

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\frac{d}{d x} (\frac{1}{4 x ^{5}})

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

Solution steps

\frac{d}{d x} (\frac{1}{4 x ^{5}})

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int_{0}^{6} 36 - x^{2} d x

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What is the derivative of 1/(\sqrt[4]{x^5}) ?
The derivative of 1/(\sqrt[4]{x^5}) is -5/(4x^{9/4)}
What is the first derivative of 1/(\sqrt[4]{x^5}) ?
The first derivative of 1/(\sqrt[4]{x^5}) is -5/(4x^{9/4)}