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Popular >

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

Solution

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

Solution

\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}}}

Graph

Popular Examples

derivative of g(x)=sqrt(8-x)derivative of

g (x) = 8 - x

tangent of f(x)=(5x-1)^{-1/6},\at x=13 tangent of

f (x) = (5 x - 1)^{- \frac{1}{6}}, at x = 13

limit as x approaches 0+of (1/x)^{3x}

x \to 0 + lim ((\frac{1}{x})^{3 x})

tangent of y=2x^2+x,(1,2)tangent of

y = 2 x^{2} + x, (1, 2)

integral from 5 to 2 of x

\int_{5}^{2} x d x

Frequently Asked Questions (FAQ)

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)}