Calculating Gradient of ln(r) in 3D Space

[brentd49]

So, the question is: find the gradient of f=ln(r), where r=sqrt(x^2+y^2+z^2)^(1/2).

For the partial with respect to x, I use the chain rule: df/dr*dr/dx.

df/dr=1/r
dr/dx=(1/2)*(2x)=x

Which would give df/dx = x/r.

But the book gets x/r^2

Where does the extra 1/r come from?

 

[hypermorphism]

So, the question is: find the gradient of f=ln(r), where r=sqrt(x^2+y^2+z^2)^(1/2).
...
dr/dx=(1/2)*(2x)=x
...

This isn't right. Remember to use the chain rule here as well.

 

[brentd49]

hah. of course. thanks