What is the derivative of f(t)=(9t+2)^{2/3} ?

The derivative of f(t)=(9t+2)^{2/3} is 6/((9t+2)^{1/3)}

What is the first derivative of f(t)=(9t+2)^{2/3} ?

The first derivative of f(t)=(9t+2)^{2/3} is 6/((9t+2)^{1/3)}

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derivative of

f (t) = (9 t + 2)^{\frac{2}{3}}

\frac{6}{( 9 t + 2 ) ^{\frac{1}{3}}}

Solution steps

\frac{d}{d t} ((9 t + 2)^{\frac{2}{3}})

Apply the chain rule:

\frac{2}{3 ( 9 t + 2 ) ^{\frac{1}{3}}} \frac{d}{d t} (9 t + 2)

= \frac{2}{3 ( 9 t + 2 ) ^{\frac{1}{3}}} \frac{d}{d t} (9 t + 2)

\frac{d}{d t} (9 t + 2) = 9

= \frac{2}{3 ( 9 t + 2 ) ^{\frac{1}{3}}} \cdot 9

Simplify

\frac{2}{3 ( 9 t + 2 ) ^{\frac{1}{3}}} \cdot 9 : \frac{6}{( 9 t + 2 ) ^{\frac{1}{3}}}

= \frac{6}{( 9 t + 2 ) ^{\frac{1}{3}}}

What is the derivative of f(t)=(9t+2)^{2/3} ?
The derivative of f(t)=(9t+2)^{2/3} is 6/((9t+2)^{1/3)}
What is the first derivative of f(t)=(9t+2)^{2/3} ?
The first derivative of f(t)=(9t+2)^{2/3} is 6/((9t+2)^{1/3)}