review question

I was wondering if you could please walk me through this problem because I cant quite seem to understand how to get it. for #4 in the 13.5 section of the final review it says let bold r= xi+yj+zk and r= I (bold r) I. then find del dot product (9 r boldr). the answer is 36r but I don't know how to get that. If you could find time to help me out id greatly appreciate it. Thank you and happy cinco de mayo haha

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So...r= xi+yj+zk is the vector and r=√(x^2+y^2+z^2) (what the textbook calls ρ-notice I didn't write this problem so I'm not the only one who prefers r to rho is three dimensions).  So we get a new vector field rxi+ryj+rzk, and

(rxi+ryj+rzk)=∂(rx)/∂x+∂(ry)/∂y+∂(rz)/∂z=(x∂r/∂x+y∂r/∂y+z∂r/∂z)+r(∂x/∂x+∂y/∂y+∂z/∂z

(by the product rule)                                        =(x∂r/∂x+y∂r/∂y+z∂r/∂z)+3rNow, ∂r/∂x=x/r, ∂r/∂y=y/r and ∂r/∂z=z/r, so (x∂r/∂x+y∂r/∂y+z∂r/∂z)= (x^2+y^2+z^2)/r=r,(rxi+ryj+rzk)=4r and so (9rr)=9x4r=36r.