What is the derivative of (x(x^2+4))^{1/3} ?

The derivative of (x(x^2+4))^{1/3} is (3x^2+4)/(3(x(x^2+4))^{2/3)}

What is the first derivative of (x(x^2+4))^{1/3} ?

The first derivative of (x(x^2+4))^{1/3} is (3x^2+4)/(3(x(x^2+4))^{2/3)}

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derivative of

(x (x^{2} + 4))^{\frac{1}{3}}

\frac{3 x ^{2} + 4}{3 ( x ( x ^{2} + 4 ) ) ^{\frac{2}{3}}}

Solution steps

\frac{d}{d x} ((x (x^{2} + 4))^{\frac{1}{3}})

Apply the chain rule:

\frac{1}{3 ( x ( x ^{2} + 4 ) ) ^{\frac{2}{3}}} \frac{d}{d x} (x (x^{2} + 4))

= \frac{1}{3 ( x ( x ^{2} + 4 ) ) ^{\frac{2}{3}}} \frac{d}{d x} (x (x^{2} + 4))

\frac{d}{d x} (x (x^{2} + 4)) = 3 x^{2} + 4

= \frac{1}{3 ( x ( x ^{2} + 4 ) ) ^{\frac{2}{3}}} (3 x^{2} + 4)

Simplify

\frac{1}{3 ( x ( x ^{2} + 4 ) ) ^{\frac{2}{3}}} (3 x^{2} + 4) : \frac{3 x ^{2} + 4}{3 ( x ( x ^{2} + 4 ) ) ^{\frac{2}{3}}}

= \frac{3 x ^{2} + 4}{3 ( x ( x ^{2} + 4 ) ) ^{\frac{2}{3}}}

\frac{\partial}{\partial x} (6 + 3 x^{2} - 2 y^{2})

\int 4 x^{2} + \frac{1}{( 2 x ) ^{2}} d x

2 t^{4}

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

\frac{6 s}{( s ^{2} - 8 s + 25 )}

What is the derivative of (x(x^2+4))^{1/3} ?
The derivative of (x(x^2+4))^{1/3} is (3x^2+4)/(3(x(x^2+4))^{2/3)}
What is the first derivative of (x(x^2+4))^{1/3} ?
The first derivative of (x(x^2+4))^{1/3} is (3x^2+4)/(3(x(x^2+4))^{2/3)}