What is the derivative of (u^{-2}+u^{-3})(u^5-6u^2) ?

The derivative of (u^{-2}+u^{-3})(u^5-6u^2) is 3u^2+2u+6/(u^2)

What is the first derivative of (u^{-2}+u^{-3})(u^5-6u^2) ?

The first derivative of (u^{-2}+u^{-3})(u^5-6u^2) is 3u^2+2u+6/(u^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

(u^{- 2} + u^{- 3}) (u^{5} - 6 u^{2})

3 u^{2} + 2 u + \frac{6}{u ^{2}}

Solution steps

\frac{d}{d u} ((u^{- 2} + u^{- 3}) (u^{5} - 6 u^{2}))

Apply the Product Rule:

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

f = u^{- 2} + u^{- 3}, g = u^{5} - 6 u^{2}

= \frac{d}{d u} (u^{- 2} + u^{- 3}) (u^{5} - 6 u^{2}) + \frac{d}{d u} (u^{5} - 6 u^{2}) (u^{- 2} + u^{- 3})

\frac{d}{d u} (u^{- 2} + u^{- 3}) = - \frac{2}{u ^{3}} - \frac{3}{u ^{4}}

\frac{d}{d u} (u^{5} - 6 u^{2}) = 5 u^{4} - 12 u

= (- \frac{2}{u ^{3}} - \frac{3}{u ^{4}}) (u^{5} - 6 u^{2}) + (5 u^{4} - 12 u) (u^{- 2} + u^{- 3})

Simplify

(- \frac{2}{u ^{3}} - \frac{3}{u ^{4}}) (u^{5} - 6 u^{2}) + (5 u^{4} - 12 u) (u^{- 2} + u^{- 3}) : 3 u^{2} + 2 u + \frac{6}{u ^{2}}

= 3 u^{2} + 2 u + \frac{6}{u ^{2}}

\int e^{- x} + 2 d x

\frac{d}{d x} (\frac{9 x}{( x ^{2} + 81 ) ^{\frac{3}{2}}})

(1 + 4 x)^{\frac{1}{2}}

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

\int 5 x^{15} e^{- x^{8}} d x

What is the derivative of (u^{-2}+u^{-3})(u^5-6u^2) ?
The derivative of (u^{-2}+u^{-3})(u^5-6u^2) is 3u^2+2u+6/(u^2)
What is the first derivative of (u^{-2}+u^{-3})(u^5-6u^2) ?
The first derivative of (u^{-2}+u^{-3})(u^5-6u^2) is 3u^2+2u+6/(u^2)