Take the derivative of rational expression

[rambo5330]

Homework Statement

f(x) = $$\frac{x}{x-1}$$ + $$\frac{x+1}{3x}$$

Homework Statement

need to take the first derivative of this expression...
I can do it but I am curious as too why i cannot take the derivative of

$$\frac{x}{x-1}$$ and then just add it to the derivative of $$\frac{x+1}{3x}$$


rather than finding a common denominator off the bat and simplifying to one expression then taking derivative of that...

I get two separate answers? the combining and simplifying method arrives at the answer in the text...

 

[Inferior89]

You can take the derivative of each and add them up. You are probably doing some arithmetic mistake.

 

[╔(σ_σ)╝]

Homework Statement

f(x) = $$\frac{x}{x-1}$$ + $$\frac{x+1}{3x}$$

Homework Statement

need to take the first derivative of this expression...
I can do it but I am curious as too why i cannot take the derivative of

$$\frac{x}{x-1}$$ and then just add it to the derivative of $$\frac{x+1}{3x}$$rather than finding a common denominator off the bat and simplifying to one expression then taking derivative of that...

I get two separate answers? the combining and simplifying method arrives at the answer in the text...

You can take the derievatives of each individual term and sum them.

My guess is that you made an error somewhere. Check your solution again or post it here. :)

EDIT

Inferior89 beat me to it :)

 

[rambo5330]

thanks I figured I could based on the rules... but I cannot see where I am making the mistake algebraically.. I'll rework again and post if i do not see the error of my ways