You need to find derivative of function using the quotient rule such that:

You need to substitute 0 for x in f'(x) such that:

**Hence, evaluating the derivative of the function at yields **

f(x) = (x-3)/(x+1)

Let f(x) = u/v such that:\

u= x-3 ==> u' = 1

v= x+1 ==> v'= 1

f'(x) = (u'v- uv')/v^2

= [1*(x+1) - (x-3)*1]/ (x+1)^2

= (x+1 - x + 3)/ (x+1)^2

= 4/(x+1)^2

f'(0) = 4/(0+1)^2 = 4/1 = 4

==> **f'(0) = 4**

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