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Popular >

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

Solution

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

Solution

\frac{4 + 45 x ^{\frac{5}{6}}}{6 3 x}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

\frac{2}{3 x ^{\frac{1}{3}}} + \frac{15 x}{2} : \frac{4 + 45 x ^{\frac{5}{6}}}{6 3 x}

= \frac{4 + 45 x ^{\frac{5}{6}}}{6 3 x}

Graph

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Frequently Asked Questions (FAQ)

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)}