How do you differentiate #f(x)=x/(x+c/x)#?

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Answer 1 · 2016-11-11T15:54:57

Start by simplifying the entire expression.

#f(x) = x/((x^2 + c)/x)#

#f(x) = x^2/(x^2 + c)#

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

#f'(x) = (2x^3 + 2xc - 2x^3)/(x^2 + c)^2#

#f'(x) = (2xc)/(x^2 + c)^2#

Hopefully this helps!