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Popular >

derivative of y=\sqrt[3]{1+4x}

Solution

derivative of

Solution

\frac{4}{3 ( 1 + 4 x ) ^{\frac{2}{3}}}

Solution steps

Apply the chain rule:

\frac{1}{3 ( 1 + 4 x ) ^{\frac{2}{3}}} \frac{d}{d x} (1 + 4 x)

= \frac{1}{3 ( 1 + 4 x ) ^{\frac{2}{3}}} \frac{d}{d x} (1 + 4 x)

\frac{d}{d x} (1 + 4 x) = 4

= \frac{1}{3 ( 1 + 4 x ) ^{\frac{2}{3}}} \cdot 4

Simplify

\frac{1}{3 ( 1 + 4 x ) ^{\frac{2}{3}}} \cdot 4 : \frac{4}{3 ( 1 + 4 x ) ^{\frac{2}{3}}}

= \frac{4}{3 ( 1 + 4 x ) ^{\frac{2}{3}}}

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Frequently Asked Questions (FAQ)

What is the derivative of y=\sqrt[3]{1+4x} ?
The derivative of y=\sqrt[3]{1+4x} is 4/(3(1+4x)^{2/3)}
What is the first derivative of y=\sqrt[3]{1+4x} ?
The first derivative of y=\sqrt[3]{1+4x} is 4/(3(1+4x)^{2/3)}