What is (\partial)/(\partial x)(\sqrt[7]{x}) ?

The answer to (\partial)/(\partial x)(\sqrt[7]{x}) is 1/(7x^{6/7)}

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(\partial)/(\partial x)(\sqrt[7]{x})

\frac{1}{7 x ^{\frac{6}{7}}}

Solution steps

Apply radical rule:

= \frac{\partial}{\partial x} (x^{\frac{1}{7}})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= \frac{1}{7} x^{\frac{1}{7} - 1}

Simplify

\frac{1}{7} x^{\frac{1}{7} - 1} : \frac{1}{7 x ^{\frac{6}{7}}}

= \frac{1}{7 x ^{\frac{6}{7}}}

3 - x

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\frac{\partial}{\partial x} (e^{- 2 x} cos (2 y))

What is (\partial)/(\partial x)(\sqrt[7]{x}) ?
The answer to (\partial)/(\partial x)(\sqrt[7]{x}) is 1/(7x^{6/7)}