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

The derivative of (x-2)^{1/3} is 1/(3(x-2)^{2/3)}

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

The first derivative of (x-2)^{1/3} is 1/(3(x-2)^{2/3)}

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derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (x - 2) = 1

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

Simplify

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

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