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Popular >

derivative of (1+3x)^{1/3}

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

What is the derivative of (1+3x)^{1/3} ?
The derivative of (1+3x)^{1/3} is 1/((1+3x)^{2/3)}
What is the first derivative of (1+3x)^{1/3} ?
The first derivative of (1+3x)^{1/3} is 1/((1+3x)^{2/3)}