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

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

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

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

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Popular >

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

\frac{d}{d x} (\frac{6 x + 8 x ^{2}}{( 3 + 8 x ) ^{2}})

f (x) = 2 x^{2} + 1

\int \frac{8 e ^{2 x}}{e ^{2 x} + 3 e ^{x} + 2} d x

6 cos (x) csc (x^{2})

cos (3 t + 5)

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