How do you differentiate #f(x)=x/(x-1)^2+x^2-4/(1-2x)# using the sum rule?

1 Answer
Bdub
Apr 14, 2016

#f'(x)=-(x+1)/(x-1)^3+2x -8/(1-2x)^2 #

Explanation:

#f(x)=x/(x-1)^2+x^2-4(1-2x)^-1#

Use Quotients Rule: #f'(x)=(gf'-fg')/g^2# to find the derivative of the first part #x/(x-1)^2#

#f'(x)=((x-1)^2-x(2(x-1)))/(x-1)^4 +2x +4/(1-2x)^2 xx-2#

#f'(x)=((x-1)[x-1-2x])/(x-1)^4 +2x +4/(1-2x)^2 xx-2#

#f'(x)=-(x+1)/(x-1)^3+2x -8/(1-2x)^2 #

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