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Question
Differentiate the following function w.r.t.x. : `1/("e"^x + 1)`
Solution
Let y = `1/(e^x + 1)`
Differentiating w.r.t. x, we get
`"dy"/"dx" = "d"/"dx" (1/("e"^x+1))`
= `(("e"^x + 1)d/dx(1) - (1)d/dx("e"^x + 1))/(("e"^x + 1)^2`
= `(("e"^x + 1)(0) - (1)("e"^x + 0))/(("e"^x + 1)^2`
= `(0 - "e"^x)/(("e"^x + 1)^2`
=`(- "e"^x)/("e"^x + 1)^2`
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