# Derivative Quesiton

find the derivative of the following:
f(x) = x/(x+c/x)

through simplication, i got:
x(x+cx^-1)^-1
=x(x^-1 + c^-1*x)
=1+1/c*x^2

taking the derivative,
-c^-2*x^2 + c^-1*2x

its wrong though so where did i go wrong?

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nothing123 said:
through simplication, i got:
x(x+cx^-1)^-1
=x(x^-1 + c^-1*x)
=1+1/c*x^2
That's not right. (x+y)-1 is not the same as x-1 + y-1.

Without simplifying the original expression you could have used the quotient rule to find the derivative, OR you could differentiate x(x+cx^-1)^-1 using the product rule.

HallsofIvy
$$f(x)= \frac{x}{x+ \frac{c}{x}}= \frac{x^2}{x^2+ c}$$