What is the derivative of (x+5^{2/3}) ?

The derivative of (x+5^{2/3}) is 2/(3(x+5)^{1/3)}

What is the first derivative of (x+5^{2/3}) ?

The first derivative of (x+5^{2/3}) is 2/(3(x+5)^{1/3)}

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\frac{d}{d x} ((x + 5)^{\frac{2}{3}})

\frac{2}{3 ( x + 5 ) ^{\frac{1}{3}}}

Solution steps

\frac{d}{d x} ((x + 5)^{\frac{2}{3}})

Apply the chain rule:

\frac{2}{3 ( x + 5 ) ^{\frac{1}{3}}} \frac{d}{d x} (x + 5)

= \frac{2}{3 ( x + 5 ) ^{\frac{1}{3}}} \frac{d}{d x} (x + 5)

\frac{d}{d x} (x + 5) = 1

= \frac{2}{3 ( x + 5 ) ^{\frac{1}{3}}} \cdot 1

Simplify

= \frac{2}{3 ( x + 5 ) ^{\frac{1}{3}}}

What is the derivative of (x+5^{2/3}) ?
The derivative of (x+5^{2/3}) is 2/(3(x+5)^{1/3)}
What is the first derivative of (x+5^{2/3}) ?
The first derivative of (x+5^{2/3}) is 2/(3(x+5)^{1/3)}