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Popular >

derivative of 4\sqrt[3]{x+8}

Solution

Solution

\frac{4}{3 ( x + 8 ) ^{\frac{2}{3}}}

Solution steps

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

Apply the chain rule:

\frac{1}{3 ( x + 8 ) ^{\frac{2}{3}}} \frac{d}{d x} (x + 8)

= \frac{1}{3 ( x + 8 ) ^{\frac{2}{3}}} \frac{d}{d x} (x + 8)

\frac{d}{d x} (x + 8) = 1

= 4 \cdot \frac{1}{3 ( x + 8 ) ^{\frac{2}{3}}} \cdot 1

Simplify

4 \cdot \frac{1}{3 ( x + 8 ) ^{\frac{2}{3}}} \cdot 1 : \frac{4}{3 ( x + 8 ) ^{\frac{2}{3}}}

= \frac{4}{3 ( x + 8 ) ^{\frac{2}{3}}}

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Frequently Asked Questions (FAQ)

What is the derivative of 4\sqrt[3]{x+8} ?
The derivative of 4\sqrt[3]{x+8} is 4/(3(x+8)^{2/3)}
What is the first derivative of 4\sqrt[3]{x+8} ?
The first derivative of 4\sqrt[3]{x+8} is 4/(3(x+8)^{2/3)}