Question

how come if \(r=|\mathbf{x}|\) then\[\frac{\partial r}{\partial\mathbf{x}}=\frac{\mathbf{x}}{r}\]

Answer 1

its true for every r,not just r = |x|
\(r= \sqrt{x^2+y^2}\)
can you diff. this w.r.t x ?

Answer 2

yes

Answer 3

yes

Answer 4

then tell me what u get ?

Answer 5

\[\frac{2x}{\sqrt{x^2+y^2}}\]

Answer 6

sorry openstudy is lagging again. I did that in my head and accidentaly multiplied by 2

Answer 7

aha I see now. thanks!

Answer 8

why is this true for any r?

Answer 9

lagging for me too....
because we haven't used r =|x| .
its like that is not given....

Answer 10

alright cool well thanks a lot!