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

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

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

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

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

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

Solution steps

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

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 = - 2, x = 1, y = 2 x^{2} + 4, y = 0

\int x^{3} cos (n x) d x

x \to - 7 lim (\frac{x}{x - 2})

e^{x} + 1

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