What is the derivative of \sqrt[3]{4x-5} ?

The derivative of \sqrt[3]{4x-5} is 4/(3(4x-5)^{2/3)}

What is the first derivative of \sqrt[3]{4x-5} ?

The first derivative of \sqrt[3]{4x-5} is 4/(3(4x-5)^{2/3)}

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derivative of

\frac{4}{3 ( 4 x - 5 ) ^{\frac{2}{3}}}

Solution steps

Apply the chain rule:

\frac{1}{3 ( 4 x - 5 ) ^{\frac{2}{3}}} \frac{d}{d x} (4 x - 5)

= \frac{1}{3 ( 4 x - 5 ) ^{\frac{2}{3}}} \frac{d}{d x} (4 x - 5)

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

= \frac{1}{3 ( 4 x - 5 ) ^{\frac{2}{3}}} \cdot 4

Simplify

\frac{1}{3 ( 4 x - 5 ) ^{\frac{2}{3}}} \cdot 4 : \frac{4}{3 ( 4 x - 5 ) ^{\frac{2}{3}}}

= \frac{4}{3 ( 4 x - 5 ) ^{\frac{2}{3}}}

What is the derivative of \sqrt[3]{4x-5} ?
The derivative of \sqrt[3]{4x-5} is 4/(3(4x-5)^{2/3)}
What is the first derivative of \sqrt[3]{4x-5} ?
The first derivative of \sqrt[3]{4x-5} is 4/(3(4x-5)^{2/3)}