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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int 0 sin (n x) d x

f (x) = 0.1 x^{3} - 0.45 x^{2} + 2.43 x + 300

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

7 x sin (x^{2})

\int - cos (x) + sin (x) + 4 d x

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