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Popular Calculus >

derivative of y=\sqrt[3]{1+5x}

Solution

derivative of

y = 3 1 + 5 x

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of y=\sqrt[3]{1+5x} ?
The derivative of y=\sqrt[3]{1+5x} is 5/(3(1+5x)^{2/3)}
What is the first derivative of y=\sqrt[3]{1+5x} ?
The first derivative of y=\sqrt[3]{1+5x} is 5/(3(1+5x)^{2/3)}