What is the derivative of f(t)=(3t+14)^{2/3} ?

The derivative of f(t)=(3t+14)^{2/3} is 2/((3t+14)^{1/3)}

What is the first derivative of f(t)=(3t+14)^{2/3} ?

The first derivative of f(t)=(3t+14)^{2/3} is 2/((3t+14)^{1/3)}

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derivative of

f (t) = (3 t + 14)^{\frac{2}{3}}

\frac{2}{( 3 t + 14 ) ^{\frac{1}{3}}}

Solution steps

\frac{d}{d t} ((3 t + 14)^{\frac{2}{3}})

Apply the chain rule:

\frac{2}{3 ( 3 t + 14 ) ^{\frac{1}{3}}} \frac{d}{d t} (3 t + 14)

= \frac{2}{3 ( 3 t + 14 ) ^{\frac{1}{3}}} \frac{d}{d t} (3 t + 14)

\frac{d}{d t} (3 t + 14) = 3

= \frac{2}{3 ( 3 t + 14 ) ^{\frac{1}{3}}} \cdot 3

Simplify

\frac{2}{3 ( 3 t + 14 ) ^{\frac{1}{3}}} \cdot 3 : \frac{2}{( 3 t + 14 ) ^{\frac{1}{3}}}

= \frac{2}{( 3 t + 14 ) ^{\frac{1}{3}}}

\frac{d y}{d x} + \frac{y}{x ^{2} + x} = x + 1

\frac{d}{d x} (2 I n x)

\frac{d}{d x} (3 e^{- 4 x})

\frac{1}{x}, 2

3 sin (- 2 x^{2})

What is the derivative of f(t)=(3t+14)^{2/3} ?
The derivative of f(t)=(3t+14)^{2/3} is 2/((3t+14)^{1/3)}
What is the first derivative of f(t)=(3t+14)^{2/3} ?
The first derivative of f(t)=(3t+14)^{2/3} is 2/((3t+14)^{1/3)}