Differentiate the following functions with respect to `x` from first principles: `(x-1)/(x+1)`

Options

A. `(x-1)/(x+1)`
B. `(x-1)/(x+1)^2`
C. `(2)/(x+1)^2`
D. None of these

Answer

C

Explanation

Let `f(x) =(x+1)/(x-1)`.


Accordingly, from the first principle,


`f'(x)= lim_(h->0) [f(x+h)-f(x)]/h`


`=lim_(h->0) [(x+h+1)/(x+h-1) - (x+1)/(x-1)]/h`


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