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

The derivative of \sqrt[3]{x^2}+sqrt(x) is (2x)/(3(x^2)^{2/3)}+1/(2sqrt(x))

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

The first derivative of \sqrt[3]{x^2}+sqrt(x) is (2x)/(3(x^2)^{2/3)}+1/(2sqrt(x))

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derivative

\frac{2 x}{3 ( x ^{2} ) ^{\frac{2}{3}}} + \frac{1}{2 x}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

What is the derivative of \sqrt[3]{x^2}+sqrt(x) ?
The derivative of \sqrt[3]{x^2}+sqrt(x) is (2x)/(3(x^2)^{2/3)}+1/(2sqrt(x))
What is the first derivative of \sqrt[3]{x^2}+sqrt(x) ?
The first derivative of \sqrt[3]{x^2}+sqrt(x) is (2x)/(3(x^2)^{2/3)}+1/(2sqrt(x))