What is the derivative of (60+2t)^{2/3} ?

The derivative of (60+2t)^{2/3} is 4/(3(60+2t)^{1/3)}

What is the first derivative of (60+2t)^{2/3} ?

The first derivative of (60+2t)^{2/3} is 4/(3(60+2t)^{1/3)}

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derivative of

(60 + 2 t)^{\frac{2}{3}}

\frac{4}{3 ( 60 + 2 t ) ^{\frac{1}{3}}}

Solution steps

\frac{d}{d t} ((60 + 2 t)^{\frac{2}{3}})

Apply the chain rule:

\frac{2}{3 ( 60 + 2 t ) ^{\frac{1}{3}}} \frac{d}{d t} (60 + 2 t)

= \frac{2}{3 ( 60 + 2 t ) ^{\frac{1}{3}}} \frac{d}{d t} (60 + 2 t)

\frac{d}{d t} (60 + 2 t) = 2

= \frac{2}{3 ( 60 + 2 t ) ^{\frac{1}{3}}} \cdot 2

Simplify

\frac{2}{3 ( 60 + 2 t ) ^{\frac{1}{3}}} \cdot 2 : \frac{4}{3 ( 60 + 2 t ) ^{\frac{1}{3}}}

= \frac{4}{3 ( 60 + 2 t ) ^{\frac{1}{3}}}

What is the derivative of (60+2t)^{2/3} ?
The derivative of (60+2t)^{2/3} is 4/(3(60+2t)^{1/3)}
What is the first derivative of (60+2t)^{2/3} ?
The first derivative of (60+2t)^{2/3} is 4/(3(60+2t)^{1/3)}