What is the derivative of \sqrt[3]{t^2}+5sqrt(t^3) ?

The derivative of \sqrt[3]{t^2}+5sqrt(t^3) is (2t}{3(t^2)^{2/3}}+\frac{15sqrt(t))/2

What is the first derivative of \sqrt[3]{t^2}+5sqrt(t^3) ?

The first derivative of \sqrt[3]{t^2}+5sqrt(t^3) is (2t}{3(t^2)^{2/3}}+\frac{15sqrt(t))/2

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derivative of

\frac{2 t}{3 ( t ^{2} ) ^{\frac{2}{3}}} + \frac{15 t}{2}

Solution steps

Apply the Sum/Difference Rule:

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

\frac{d}{d t} (5 t^{3}) = \frac{15 t}{2}

= \frac{2 t}{3 ( t ^{2} ) ^{\frac{2}{3}}} + \frac{15 t}{2}

What is the derivative of \sqrt[3]{t^2}+5sqrt(t^3) ?
The derivative of \sqrt[3]{t^2}+5sqrt(t^3) is (2t}{3(t^2)^{2/3}}+\frac{15sqrt(t))/2
What is the first derivative of \sqrt[3]{t^2}+5sqrt(t^3) ?
The first derivative of \sqrt[3]{t^2}+5sqrt(t^3) is (2t}{3(t^2)^{2/3}}+\frac{15sqrt(t))/2