Product rule instead of quotient rule?

[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?

 

[AKG]

Yes.....

 

[Hurkyl]

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

 

[leon1127]

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