How do you differentiate $y=e^x/(1+x)$ ?

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Answer 1 · 2016-12-25T08:21:18

The answer is $=(xe^x)/(1+x)^2$

We need the differentiation of a quotient

$(u/v)'=(u'v-uv')/v^2$

Here, $u=e^x$ , $=>$ , $u'=e^x$

$v=1+x$ , $=>$ , $v'=1$

Therefore,

$dy/dx=(e^x(x+1)-e^x)/(1+x)^2$

$=(xe^x+e^x-e^x)/(1+x)^2$

$=(xe^x)/(1+x)^2$

How do you differentiate y=e^x/(1+x)y=e^x/(1+x)?