Thursday, 25 August 2016

calculus - What is the derivative of fracx2+2xx2cdot2x at 1?



Let there be f(x)=x2+2xx22x
I'm asked to calculate f(1). I know that I should apply the division rule, then find the derivative f(x) while applying power, chain and product rules when necessary, and finally evaluate f(1).



The thing is all these steps seemed way to lengthy to me. I figured out that maybe there somehow was a shorter way to find f(x) without going through all these lengthy calculations.



Any help would be appreciated and thanks in advance.


Answer



Note that f(x)=x2+2xx22x=2x+x2.



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