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

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

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

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

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derivative of

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

\frac{2 - 5 x}{3 x ^{\frac{1}{3}}}

Solution steps

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

Apply the Product Rule:

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

f = x^{\frac{2}{3}}, g = 1 - x

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

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

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

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

Simplify

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

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

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