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Popular >

derivative of \sqrt[3]{9x+1}

Solution

\frac{d}{d x} (3 9 x + 1)

Solution

\frac{3}{( 9 x + 1 ) ^{\frac{2}{3}}}

Solution steps

\frac{d}{d x} (3 9 x + 1)

Apply the chain rule:

\frac{1}{3 ( 9 x + 1 ) ^{\frac{2}{3}}} \frac{d}{d x} (9 x + 1)

= \frac{1}{3 ( 9 x + 1 ) ^{\frac{2}{3}}} \frac{d}{d x} (9 x + 1)

\frac{d}{d x} (9 x + 1) = 9

= \frac{1}{3 ( 9 x + 1 ) ^{\frac{2}{3}}} \cdot 9

Simplify

\frac{1}{3 ( 9 x + 1 ) ^{\frac{2}{3}}} \cdot 9 : \frac{3}{( 9 x + 1 ) ^{\frac{2}{3}}}

= \frac{3}{( 9 x + 1 ) ^{\frac{2}{3}}}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of \sqrt[3]{9x+1} ?
The derivative of \sqrt[3]{9x+1} is 3/((9x+1)^{2/3)}
What is the first derivative of \sqrt[3]{9x+1} ?
The first derivative of \sqrt[3]{9x+1} is 3/((9x+1)^{2/3)}