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

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

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

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

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

Solution steps

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int 2 x (x^{2} + 5)^{8} d x

\int 11 x d x

\frac{d}{d x} (2^{x} - 1)

\int 48 sec^{4} (x) d x

\frac{d y}{d t} + e^{t} y = - 2 e^{t}

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