Differentiate-x-1-x-4-

Question Number 37730 by Rio Mike last updated on 17/Jun/18

D i f f e r e n t i a t e

x {(1 + x)}^{4}

Commented by Rio Mike last updated on 17/Jun/18

l e t u = x \Rightarrow \frac{d u}{d x} = 1

v = {(1 + x)}^{4} \Rightarrow \frac{d v}{d x} = 4 {(1 + x)}^{3}

\frac{d (u v)}{d x} = u \frac{d v}{d x} + v \frac{d u}{d x}

= x (4 {(1 + x)}^{3}) + {(1 + x)}^{4} 1

= 4 x {(1 + x)}^{3} + 1 + x

Answered by MJS last updated on 17/Jun/18

{(u v)}^{'} = u^{'} v + {u v}^{'}

\frac{d}{d x} [x {(x + 1)}^{4}] = {(x + 1)}^{4} + 4 {(x + 1)}^{3} = (x + 5) {(x + 1)}^{3}

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