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

The derivative of x^{2/3}(5-x) is (10-5x)/(3x^{1/3)}

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

The first derivative of x^{2/3}(5-x) is (10-5x)/(3x^{1/3)}

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

\frac{10 - 5 x}{3 x ^{\frac{1}{3}}}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

\frac{2}{3 x ^{\frac{1}{3}}} (5 - x) + (- 1) x^{\frac{2}{3}} : \frac{10 - 5 x}{3 x ^{\frac{1}{3}}}

= \frac{10 - 5 x}{3 x ^{\frac{1}{3}}}

19 - x^{2}, - 2 x + 16, - 5, - 19

\frac{\partial}{\partial x} (y \cdot ∣ x ∣)

(x^{2} + 1) y^{^{'}} + 9 x (y - 1) = 0, y (0) = 2

\frac{d P}{d t} - a P = b

d x + e^{9 x} d y = 0

What is the derivative of x^{2/3}(5-x) ?
The derivative of x^{2/3}(5-x) is (10-5x)/(3x^{1/3)}
What is the first derivative of x^{2/3}(5-x) ?
The first derivative of x^{2/3}(5-x) is (10-5x)/(3x^{1/3)}