What is the derivative of f(t)=t^{2/3}-t^{1/3}+4 ?

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

What is the first derivative of f(t)=t^{2/3}-t^{1/3}+4 ?

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

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derivative of

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

\frac{2}{3 t ^{\frac{1}{3}}} - \frac{1}{3 t ^{\frac{2}{3}}}

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

\frac{d}{d t} (4) = 0

= \frac{2}{3 t ^{\frac{1}{3}}} - \frac{1}{3 t ^{\frac{2}{3}}} + 0

Simplify

= \frac{2}{3 t ^{\frac{1}{3}}} - \frac{1}{3 t ^{\frac{2}{3}}}

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