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

The derivative of \sqrt[3]{x^2}+5sqrt(x^3) is (4+45x^{5/6})/(6\sqrt[3]{x)}

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

The first derivative of \sqrt[3]{x^2}+5sqrt(x^3) is (4+45x^{5/6})/(6\sqrt[3]{x)}

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Solution steps

Apply the Sum/Difference Rule:

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

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

= \frac{2}{3 x ^{\frac{1}{3}}} + \frac{15 x}{2}

Simplify

What is the derivative of \sqrt[3]{x^2}+5sqrt(x^3) ?
The derivative of \sqrt[3]{x^2}+5sqrt(x^3) is (4+45x^{5/6})/(6\sqrt[3]{x)}
What is the first derivative of \sqrt[3]{x^2}+5sqrt(x^3) ?
The first derivative of \sqrt[3]{x^2}+5sqrt(x^3) is (4+45x^{5/6})/(6\sqrt[3]{x)}