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Question
Find the derivative of the following function (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
`(1 + 1/x)/(1- 1/x)`
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Solution
Let f(x) = `(1 + 1/x)/(1 - 1/x) = ((x + 1)/x)/((x - 1)/x) = (x + 1)/(x - 1)`
∴ `f'(x) = ([d/dx (x + 1)] (x - 1) - (x + 1) d/dx (x - 1))/(x - 1)^2`
= `(1. (x - 1) - (x + 1). 1)/(x - 1)^2`
= `(x - 1 - x - 1)/(x - 1)^2`
= `(-2)/(x - 1)^2`
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