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

The derivative of x^{2/3}(x-4) is (5x-8)/(3x^{1/3)}

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

The first derivative of x^{2/3}(x-4) is (5x-8)/(3x^{1/3)}

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\frac{d}{d x} (x^{\frac{2}{3}} (x - 4))

\frac{5 x - 8}{3 x ^{\frac{1}{3}}}

Solution steps

\frac{d}{d x} (x^{\frac{2}{3}} (x - 4))

Apply the Product Rule:

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

f = x^{\frac{2}{3}}, g = x - 4

= \frac{d}{d x} (x^{\frac{2}{3}}) (x - 4) + \frac{d}{d x} (x - 4) x^{\frac{2}{3}}

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

\frac{d}{d x} (x - 4) = 1

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

Simplify

\frac{2}{3 x ^{\frac{1}{3}}} (x - 4) + 1 \cdot x^{\frac{2}{3}} : \frac{5 x - 8}{3 x ^{\frac{1}{3}}}

= \frac{5 x - 8}{3 x ^{\frac{1}{3}}}

\frac{d}{d x} ((2 x - 8)^{5})

f (t) = t^{2} e^{3 t}

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

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

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

What is the derivative of x^{2/3}(x-4) ?
The derivative of x^{2/3}(x-4) is (5x-8)/(3x^{1/3)}
What is the first derivative of x^{2/3}(x-4) ?
The first derivative of x^{2/3}(x-4) is (5x-8)/(3x^{1/3)}