What is the derivative of (x^3+7)^{2/3} ?

The derivative of (x^3+7)^{2/3} is (2x^2)/((x^3+7)^{1/3)}

What is the first derivative of (x^3+7)^{2/3} ?

The first derivative of (x^3+7)^{2/3} is (2x^2)/((x^3+7)^{1/3)}

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derivative of

(x^{3} + 7)^{\frac{2}{3}}

\frac{2 x ^{2}}{( x ^{3} + 7 ) ^{\frac{1}{3}}}

Solution steps

\frac{d}{d x} ((x^{3} + 7)^{\frac{2}{3}})

Apply the chain rule:

\frac{2}{3 ( x ^{3} + 7 ) ^{\frac{1}{3}}} \frac{d}{d x} (x^{3} + 7)

= \frac{2}{3 ( x ^{3} + 7 ) ^{\frac{1}{3}}} \frac{d}{d x} (x^{3} + 7)

\frac{d}{d x} (x^{3} + 7) = 3 x^{2}

= \frac{2}{3 ( x ^{3} + 7 ) ^{\frac{1}{3}}} \cdot 3 x^{2}

Simplify

\frac{2}{3 ( x ^{3} + 7 ) ^{\frac{1}{3}}} \cdot 3 x^{2} : \frac{2 x ^{2}}{( x ^{3} + 7 ) ^{\frac{1}{3}}}

= \frac{2 x ^{2}}{( x ^{3} + 7 ) ^{\frac{1}{3}}}

f (x) = - 3 x^{2} - 3 x + 2, at x = 1

f (x) = 3 x^{2} + e^{2 x} + π^{2}

\frac{d}{d x} (16 - x^{2})

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

7 x 3 x

What is the derivative of (x^3+7)^{2/3} ?
The derivative of (x^3+7)^{2/3} is (2x^2)/((x^3+7)^{1/3)}
What is the first derivative of (x^3+7)^{2/3} ?
The first derivative of (x^3+7)^{2/3} is (2x^2)/((x^3+7)^{1/3)}