What is the derivative of (x^3-8)^{2/3} ?

The derivative of (x^3-8)^{2/3} is (2x^2)/((x^3-8)^{1/3)}

What is the first derivative of (x^3-8)^{2/3} ?

The first derivative of (x^3-8)^{2/3} is (2x^2)/((x^3-8)^{1/3)}

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derivative of

(x^{3} - 8)^{\frac{2}{3}}

\frac{2 x ^{2}}{( x ^{3} - 8 ) ^{\frac{1}{3}}}

Solution steps

\frac{d}{d x} ((x^{3} - 8)^{\frac{2}{3}})

Apply the chain rule:

\frac{2}{3 ( x ^{3} - 8 ) ^{\frac{1}{3}}} \frac{d}{d x} (x^{3} - 8)

= \frac{2}{3 ( x ^{3} - 8 ) ^{\frac{1}{3}}} \frac{d}{d x} (x^{3} - 8)

\frac{d}{d x} (x^{3} - 8) = 3 x^{2}

= \frac{2}{3 ( x ^{3} - 8 ) ^{\frac{1}{3}}} \cdot 3 x^{2}

Simplify

\frac{2}{3 ( x ^{3} - 8 ) ^{\frac{1}{3}}} \cdot 3 x^{2} : \frac{2 x ^{2}}{( x ^{3} - 8 ) ^{\frac{1}{3}}}

= \frac{2 x ^{2}}{( x ^{3} - 8 ) ^{\frac{1}{3}}}

\frac{d}{d a} (sin (a) + sin (2 a) + sin (3 a))

- \frac{5 s}{( s ^{2} + 1 ) ^{2}}

\int (x + 1) (x + 3) d x

\frac{- 0.1 s}{s ^{2} - 9.8}

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

What is the derivative of (x^3-8)^{2/3} ?
The derivative of (x^3-8)^{2/3} is (2x^2)/((x^3-8)^{1/3)}
What is the first derivative of (x^3-8)^{2/3} ?
The first derivative of (x^3-8)^{2/3} is (2x^2)/((x^3-8)^{1/3)}