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

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Answer 1 · 2015-12-20T17:43:14

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

Rewrite using logarithm rules.

#f(x)=x+2lnx-x^2#

The sum rule simply means that you can take the derivative of each individual part and then add them together.

#d/dx[x]=1#

#d/dx[2lnx]=2d/dx[lnx]=2(1/x)=2/x#

#d/dx[x^2]=2x#

Thus,

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

Simplified:

#f'(x)=-(2x^2-x-2)/x#