What is the derivative of \sqrt[3]{x^2+4} ?

The derivative of \sqrt[3]{x^2+4} is (2x)/(3(x^2+4)^{2/3)}

What is the first derivative of \sqrt[3]{x^2+4} ?

The first derivative of \sqrt[3]{x^2+4} is (2x)/(3(x^2+4)^{2/3)}

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derivative of

3 x^{2} + 4

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \to 0 lim (\frac{( e ^{x} - e ^{- x} - 2 x )}{( x - sin ( x ) )})

y = \frac{1}{arctan ( x )}

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

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

\int_{- 2}^{2} 4 d x

What is the derivative of \sqrt[3]{x^2+4} ?
The derivative of \sqrt[3]{x^2+4} is (2x)/(3(x^2+4)^{2/3)}
What is the first derivative of \sqrt[3]{x^2+4} ?
The first derivative of \sqrt[3]{x^2+4} is (2x)/(3(x^2+4)^{2/3)}