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