What is the derivative of \sqrt[3]{x+3} ?

The derivative of \sqrt[3]{x+3} is 1/(3(x+3)^{2/3)}

What is the first derivative of \sqrt[3]{x+3} ?

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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