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

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

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

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

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derivative

\frac{5}{3 ( 5 x + 3 ) ^{\frac{2}{3}}}

Solution steps

\frac{d}{d x} (3 5 x + 3)

Apply the chain rule:

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

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

\frac{d}{d x} (5 x + 3) = 5

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

Simplify

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

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

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