What is the derivative of 1/(\sqrt[7]{x}) ?

The derivative of 1/(\sqrt[7]{x}) is -1/(7x^{8/7)}

What is the first derivative of 1/(\sqrt[7]{x}) ?

The first derivative of 1/(\sqrt[7]{x}) is -1/(7x^{8/7)}

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- \frac{1}{7 x ^{\frac{8}{7}}}

Solution steps

Apply exponent rule:

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

= \frac{d}{d 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{8}{7}}}

= - \frac{1}{7 x ^{\frac{8}{7}}}

x \to 2 - lim (2 - x - 2)

\int \frac{8 t - 3}{t + 1} d t

x \to 4 lim (x^{2} + 5 - x)

t^{2} y^{^{''}} + 3 t y^{^{'}} - 8 y = 0

\frac{\partial}{\partial y} (x^{4} + x^{2} y)

What is the derivative of 1/(\sqrt[7]{x}) ?
The derivative of 1/(\sqrt[7]{x}) is -1/(7x^{8/7)}
What is the first derivative of 1/(\sqrt[7]{x}) ?
The first derivative of 1/(\sqrt[7]{x}) is -1/(7x^{8/7)}