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Popular >

derivative of (4x-3^{1/3})

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

What is the derivative of (4x-3^{1/3}) ?
The derivative of (4x-3^{1/3}) is 4/(3(4x-3)^{2/3)}
What is the first derivative of (4x-3^{1/3}) ?
The first derivative of (4x-3^{1/3}) is 4/(3(4x-3)^{2/3)}