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Popular >

derivative of x^{2/5}(x-5)

Solution

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

Solution

\frac{7 x - 10}{5 x ^{\frac{3}{5}}}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

\frac{2}{5 x ^{\frac{3}{5}}} (x - 5) + 1 \cdot x^{\frac{2}{5}} : \frac{7 x - 10}{5 x ^{\frac{3}{5}}}

= \frac{7 x - 10}{5 x ^{\frac{3}{5}}}

Graph

Popular Examples

y^{''}-6y^'=36t,y(0)=6,y^'(0)=0

y^{^{''}} - 6 y^{^{'}} = 36 t, y (0) = 6, y^{^{'}} (0) = 0

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\int_{0}^{8} x^{3} e^{x} d x

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

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\frac{x - 4}{x + 4}

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Frequently Asked Questions (FAQ)

What is the derivative of x^{2/5}(x-5) ?
The derivative of x^{2/5}(x-5) is (7x-10)/(5x^{3/5)}
What is the first derivative of x^{2/5}(x-5) ?
The first derivative of x^{2/5}(x-5) is (7x-10)/(5x^{3/5)}