f(x)= x^2 / (x-2)    find 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

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