Question

given f(x)+ (x)/(x+(2/X))
The derivative of the function is given by
f'(x)= (Ax^2+Bx+c)/(x^2+D)^2
where
A=__ B=__C=__D=__
Everytime I try to use the quotient rule I dont come up with the correct answer. How do I do this? Can you please show each step?
Thank you

Answer 1

typo the F(x)+ is supposed to be an = not a +

Answer 2

\[ \large f(x)=\frac{x}{x+\frac{2}{x}} \]
??

Answer 3

yes

Answer 4

then after some operations:
\[ \large f(x)=\frac{x^2}{x^2+2} \]
agree?

Answer 5

how did you get that?

Answer 6

add the fractions in the denominator. and then use this
\[ \large \frac{a/b}{c/d}=\frac{ad}{bc} \]

Answer 7

use quotient rule:\[f'(x)=\frac{1(x+\frac{2}{x})-x(1-\frac{2}{x^2})}{(x+\frac{2}{x})^2}\]go from there

Answer 8

Yeah, better to simplify first as per @helder_edwin

Answer 9

then use quotient rule:\[f'(x)=\frac{2x(x^2+2)-x^2(2x)}{(x^2+2)^2}\]go fro, there...

Answer 10

thanks guys! I didnt simplify before I tried using the quotient rule so I think that's where i went wrong

Answer 11

Yeah, if you don't simplify before hand it is easy to make a mistake...the calculation is much messier.