Question

Differentiate f(x) = x / (x + c/x)

Answer 1

\[f(x)=\frac{x^2}{x^2+c}\]

Answer 2

f(x)=x^2/c+x^2
c/c+2x^2f(x)=1

Answer 3

\[\frac{2x(x^2+c)-x^2(2x)}{(x^2+c)^2}\]

Answer 4

use the quotient rule

u = x^2 du/dx = 2x

v = x^2 + c dv/dx = 2x

dy/dx = {(x^2 +c)2x - (x^2)2x}/(x^2 + c)^2

you can simplify it

Answer 5

\[\frac{2xc}{(x^2+c)^2}\]