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

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

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

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

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\frac{d}{d x} (x^{\frac{2}{3}} (\frac{5}{2} - x))

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

Solution steps

\frac{d}{d x} (x^{\frac{2}{3}} (\frac{5}{2} - x))

Apply the Product Rule:

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

f = x^{\frac{2}{3}}, g = \frac{5}{2} - x

= \frac{d}{d x} (x^{\frac{2}{3}}) (\frac{5}{2} - x) + \frac{d}{d x} (\frac{5}{2} - x) x^{\frac{2}{3}}

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

\frac{d}{d x} (\frac{5}{2} - x) = - 1

= \frac{2}{3 x ^{\frac{1}{3}}} (\frac{5}{2} - x) + (- 1) x^{\frac{2}{3}}

Simplify

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

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

\frac{2 x + 3}{3 x - 2}

sin (9 x) sin (2 x)

x \to \infty lim (2 (x)^{2})

\int \frac{5}{x ^{2} - 36} d x

\frac{\partial}{\partial t} (3 t^{2})

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