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

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

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

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

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derivative of

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

3 u^{2} + 2 u - \frac{5}{u ^{2}}

Solution steps

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

Apply the Product Rule:

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

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

= \frac{d}{d u} (u^{- 2} + u^{- 3}) (u^{5} + 5 u^{2}) + \frac{d}{d u} (u^{5} + 5 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} + 5 u^{2}) = 5 u^{4} + 10 u

= (- \frac{2}{u ^{3}} - \frac{3}{u ^{4}}) (u^{5} + 5 u^{2}) + (5 u^{4} + 10 u) (u^{- 2} + u^{- 3})

Simplify

(- \frac{2}{u ^{3}} - \frac{3}{u ^{4}}) (u^{5} + 5 u^{2}) + (5 u^{4} + 10 u) (u^{- 2} + u^{- 3}) : 3 u^{2} + 2 u - \frac{5}{u ^{2}}

= 3 u^{2} + 2 u - \frac{5}{u ^{2}}

\frac{d}{d x} (tan^{2} (x θ))

\int_{1}^{e^{5}} \frac{5}{x} d x

f (x) = 1 + 4 - x, at x = 2

x \to \infty lim ((x) 3)

cos (2 x), 0

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