f(x) = x^2 /(x-2)
We know that if f= u/v , then f'= (u'v-uv')/v^2
Now we will assume that:
u= x^2 ==> u'=2x
v= x-2 ==> v' =1
Then f'(x) = [2x(x-2)- x^2(1)]/(x-2)^2
= (2x^2 -4x -x^2 )/(x-2)^2
= (x^2 -4x)/(x-2)^2
Now we will substitute with x=1
f'(1)...
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f(x) = x^2 /(x-2)
We know that if f= u/v , then f'= (u'v-uv')/v^2
Now we will assume that:
u= x^2 ==> u'=2x
v= x-2 ==> v' =1
Then f'(x) = [2x(x-2)- x^2(1)]/(x-2)^2
= (2x^2 -4x -x^2 )/(x-2)^2
= (x^2 -4x)/(x-2)^2
Now we will substitute with x=1
f'(1) = (1-4)/(1-2)^2
= -3/ 1= -3
Then f'(1)= -3