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Popular >

derivative of f(x)= 1/(\sqrt[3]{2x-1)}

Solution

derivative of

Solution

- \frac{2}{3 ( 2 x - 1 ) ^{\frac{4}{3}}}

Solution steps

Apply exponent rule:

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

= \frac{d}{d x} ((2 x - 1)^{- \frac{1}{3}})

Apply the chain rule:

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

= - \frac{1}{3 ( 2 x - 1 ) ^{\frac{4}{3}}} \frac{d}{d x} (2 x - 1)

\frac{d}{d x} (2 x - 1) = 2

= - \frac{1}{3 ( 2 x - 1 ) ^{\frac{4}{3}}} \cdot 2

Simplify

- \frac{1}{3 ( 2 x - 1 ) ^{\frac{4}{3}}} \cdot 2 : - \frac{2}{3 ( 2 x - 1 ) ^{\frac{4}{3}}}

= - \frac{2}{3 ( 2 x - 1 ) ^{\frac{4}{3}}}

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\frac{\partial}{\partial u ( v )} (\frac{e ^{v}}{u ( v ) + v ^{3}})

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)= 1/(\sqrt[3]{2x-1)} ?
The derivative of f(x)= 1/(\sqrt[3]{2x-1)} is -2/(3(2x-1)^{4/3)}
What is the first derivative of f(x)= 1/(\sqrt[3]{2x-1)} ?
The first derivative of f(x)= 1/(\sqrt[3]{2x-1)} is -2/(3(2x-1)^{4/3)}