What is the derivative of \sqrt[3]{x^3+1} ?

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

What is the first derivative of \sqrt[3]{x^3+1} ?

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

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derivative of

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

Solution steps

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \to - 2 lim ((x + 1)^{5} (5 x^{2}))

\int 3 - 2 x d x

\frac{d}{d θ} (10 sin (θ))

\frac{d}{d x} (ln (\frac{3 e ^{x}}{2 x ^{2}}))

x \to \infty lim (e^{x l n (\frac{3}{5})})

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