Question

Derivative checking
Find derivative \(\dfrac{x}{x+(c/x)}\)
Need help on figure out the mistake

Answer 1

\(f(x)=\dfrac{x}{x+cx^{-1}}\\f'(x) = \dfrac{(x+c/x)-(x) (1-cx^{-2})}{(x+(c/x))^2}=\dfrac{2c}{x(x+(c/x))^2}\)

Answer 2

perhaps it would be better to simplify.

\(\large\color{black}{ \displaystyle \frac{ x }{x+\frac{c}{x}} }\)

\(\large\color{black}{ \displaystyle \frac{ x }{\frac{x^2}{x}+\frac{c}{x}} }\)

\(\large\color{black}{ \displaystyle \frac{ x }{\frac{x^2+c}{x}} }\)

\(\large\color{black}{ \displaystyle \frac{ x^2 }{x^2+c} }\).

Answer 3

but other student gave me the solution above and I didn't find out what is wrong with it.

Answer 4

oh, I found it out.

Answer 5

\(\large\color{black}{ \displaystyle \frac{ (x+\frac{c}{x})-x(1-\frac{c}{x^2})}{(x+\frac{c}{x})^2} }\)

\(\large\color{black}{ \displaystyle \frac{ x+\frac{c}{x}-x+\frac{c}{x}}{(x+\frac{c}{x})^2} }\)

\(\large\color{black}{ \displaystyle \frac{ \frac{2c}{x}}{(x+\frac{c}{x})^2} }\)

\(\large\color{black}{ \displaystyle \frac{2c}{x(x+\frac{c}{x})^2} }\)

Answer 6

Actually, I made mistake at somewhere.

Answer 7

yes, you are lacking x on bottom

Answer 8

Nothing is wrong, the answers are same

Answer 9

I would rather work out (x^2)/(x^2+c)

Answer 10

Thanks a lot

Answer 11

just as a matter of preference

Answer 12

np