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

The derivative of x^{2/3}(x-2) is (5x-4)/(3x^{1/3)}

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

The first derivative of x^{2/3}(x-2) is (5x-4)/(3x^{1/3)}

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

\frac{5 x - 4}{3 x ^{\frac{1}{3}}}

Solution steps

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

Apply the Product Rule:

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

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

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

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

Simplify

\frac{2}{3 x ^{\frac{1}{3}}} (x - 2) + 1 \cdot x^{\frac{2}{3}} : \frac{5 x - 4}{3 x ^{\frac{1}{3}}}

= \frac{5 x - 4}{3 x ^{\frac{1}{3}}}

y^{^{'}} = \frac{3 x ^{2} + y ^{2}}{x y}

ln (sec (2 x) + tan (2 x))

(- 3, - 9), (8, 3)

f (x) = 3 x^{2} e^{x} + e^{x} (x^{3} + 9)

y \frac{d y}{d x} = \frac{4}{5} x

What is the derivative of x^{2/3}(x-2) ?
The derivative of x^{2/3}(x-2) is (5x-4)/(3x^{1/3)}
What is the first derivative of x^{2/3}(x-2) ?
The first derivative of x^{2/3}(x-2) is (5x-4)/(3x^{1/3)}