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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} (5^{s i n (x)})

\frac{d}{d x} (x^{2} cos^{2} (x))

\frac{d y}{d t} = 2 t

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

\frac{d y}{d t} = e^{- 3 t}, y (0) = 10

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