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Question
Differentiate the following function w.r.t.x. : `((2"e"^x - 1))/((2"e"^x + 1))`
Solution
Let y =`(2"e"^x - 1)/(2"e"^x + 1)`
Differentiating w.r.t. x, we get
`dy/dx=d/dx((2"e"^x - 1)/(2"e"^x + 1))`
= `((2"e"^x + 1)d/dx(2"e"^x - 1) - (2"e"^x - 1)d/dx(2"e"^x + 1))/((2"e"^x + 1)^2)`
= `((2"e"^x + 1)(2"e"^x - 0) - (2"e"^x - 1)(2"e"^x))/((2"e"^x + 1)^2)`
= `((2"e" + 1)(2"e"^x) - (2"e"^x - 1)(2"e"^x))/((2"e"^x - 1))`
= `(2"e"^x(2"e"^x + 1 - 2"e"^x + 1))/((2"e"^x + 1)^2)`
= `(2"e"^x(2))/((2"e"^x + 1)^2`
= `(4"e"^x)/(2"e"^x + 1)^2`
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