Finding d/dx Given d/dr and a Change of Variable

[M. next]

let x=r^2.
if we have already d/dr, how to find d/dx?

I was saying, d/dr=(d/dx)*(dx/dr)=(d/dx)*2r ?

But am doubting it?

 

[tiny-tim]

Hi M. next!

(try using the X² button just above the Reply box )

I was saying, d/dr=(d/dx)*(dx/dr)=(d/dx)*2r ?

Yes, that's a correct use of the chain rule, it's fine.

(though i'd write it 2r*dr/dx, to leave the d/dx free to have-a-go at the next thing! )

 

[M. next]

Thanks Tim :) but my doubting results from.. Well, I recall from class that there was a radical 2 and not only 2?

 

[tiny-tim]

√2 ?

i can't think where that would come from

 

[M. next]

Neither could I, thanks tim,
have a good day