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

The derivative of x^{3/5}(4-x) is (12-8x)/(5x^{2/5)}

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

The first derivative of x^{3/5}(4-x) is (12-8x)/(5x^{2/5)}

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\frac{d}{d x} (x^{\frac{3}{5}} (4 - x))

\frac{12 - 8 x}{5 x ^{\frac{2}{5}}}

Solution steps

\frac{d}{d x} (x^{\frac{3}{5}} (4 - x))

Apply the Product Rule:

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

f = x^{\frac{3}{5}}, g = 4 - x

= \frac{d}{d x} (x^{\frac{3}{5}}) (4 - x) + \frac{d}{d x} (4 - x) x^{\frac{3}{5}}

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

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

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

Simplify

\frac{3}{5 x ^{\frac{2}{5}}} (4 - x) + (- 1) x^{\frac{3}{5}} : \frac{12 - 8 x}{5 x ^{\frac{2}{5}}}

= \frac{12 - 8 x}{5 x ^{\frac{2}{5}}}

arccos (e^{2 x})

\int_{0}^{2} \frac{1}{x ^{1.9}} d x

f (x) = \frac{x + 3}{x + 5}

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

\int_{0}^{\frac{π}{2}} π cos^{2} (x) d x

What is the derivative of x^{3/5}(4-x) ?
The derivative of x^{3/5}(4-x) is (12-8x)/(5x^{2/5)}
What is the first derivative of x^{3/5}(4-x) ?
The first derivative of x^{3/5}(4-x) is (12-8x)/(5x^{2/5)}