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

The derivative of x^{2/3}(x^2-8) is (8x^2-16)/(3x^{1/3)}

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

The first derivative of x^{2/3}(x^2-8) is (8x^2-16)/(3x^{1/3)}

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

\frac{8 x ^{2} - 16}{3 x ^{\frac{1}{3}}}

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{\frac{2}{3}}, g = x^{2} - 8

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

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

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

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

Simplify

\frac{2}{3 x ^{\frac{1}{3}}} (x^{2} - 8) + 2 x x^{\frac{2}{3}} : \frac{8 x ^{2} - 16}{3 x ^{\frac{1}{3}}}

= \frac{8 x ^{2} - 16}{3 x ^{\frac{1}{3}}}

(x + 6) e^{3 x} + 4

\int 2^{x} sin (x) d x

x \to 2 lim (x^{2} + 3 x)

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

\frac{4}{9 ( s + 1 ) ( s + 2 ) ^{3}}

What is the derivative of x^{2/3}(x^2-8) ?
The derivative of x^{2/3}(x^2-8) is (8x^2-16)/(3x^{1/3)}
What is the first derivative of x^{2/3}(x^2-8) ?
The first derivative of x^{2/3}(x^2-8) is (8x^2-16)/(3x^{1/3)}