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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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