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Question
Differentiate the following with respect to x.
`e^x/(1 + x)`
Solution
Let y = `e^x/(1 + x)`
`"dy"/"dx" = (1 + x "d"/"dx" (e^x) - e^x "d"/"dx" (1 + x))/(1 + x)^2`
`= ((1 + x)e^x - e^x * 1)/(1 + x)^2`
`= (e^x (1 + x - 1))/(1 + x)^2`
`= (xe^x)/(1 + x)^2`
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