Product rule instead of quotient rule?

1. Mar 19, 2006

Flatland

Say for example, to differentiate x/(x²+1) I would use to quotient rule. However, would it be legal to bring up the denominator to: (x)(x²+1)-¹ and use the product/chain rule instead?

2. Mar 19, 2006

AKG

Yes..............

3. Mar 19, 2006

Hurkyl

Staff Emeritus
Sure. As an exercise, try deriving the quotient rule using that trick.

4. Mar 19, 2006

leon1127

yes, they are the same. if you need not simplify, i think that way is even easier.