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

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

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

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

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derivative of

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

Solution steps

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int \frac{1}{cos ( x )} d x

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x y^{^{'}} - y = 3 x ln (x)

\frac{1}{10} x^{5} - 3 x^{3}

\int \frac{3 x - 11}{x ^{3} - 5 x ^{2}} d x

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