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