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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} ((x^{3} + 1)^{2}) = 6 x^{2} (x^{3} + 1)

= \frac{1}{3 ( ( x ^{3} + 1 ) ^{2} ) ^{\frac{2}{3}}} \cdot 6 x^{2} (x^{3} + 1)

Simplify

\frac{1}{3 ( ( x ^{3} + 1 ) ^{2} ) ^{\frac{2}{3}}} \cdot 6 x^{2} (x^{3} + 1) : \frac{2 x ^{2} ( x ^{3} + 1 )}{( ( x ^{3} + 1 ) ^{2} ) ^{\frac{2}{3}}}

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

t \to 0 lim (e^{- s t})

\int 1 + 25 x^{2} d x

\frac{d}{d x} (x^{2} sin (6 x))

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

\frac{d}{d x} (cos (x) \cdot sin (x))

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