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

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

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

$$letu=x\Rightarrow \frac{du}{dx}=1$$$$v={(1+x)}^4\Rightarrow \frac{dv}{dx}=4{(1+x)}^3$$$$\frac{d\left(uv\right)}{dx}=u\frac{dv}{dx}+v\frac{du}{dx}$$$$=x\left(4{(1+x)}^3\right)+{(1+x)}^{4}1$$$$=4x{(1+x)}^3+1+x$$$$$$

Answered by MJS last updated on 17/Jun/18

$${\left(uv\right)}^{\prime }=u^{\prime }v+{uv}^{\prime }$$$$\frac{d}{dx}\left[x{(x+1)}^4\right]={(x+1)}^4+4{(x+1)}^3=(x+5){(x+1)}^3$$

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