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Popular >

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

Solution

derivative of

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

Popular Examples

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\int \frac{1}{( 4 x ^{2} - 24 x + 27 ) ^{\frac{3}{2}}} d x

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

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integral from-4 to 4 of sqrt(3)(16-y^2)

\int_{- 4}^{4} 3 (16 - y^{2}) d y

Frequently Asked Questions (FAQ)

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