Answer to Question #97197 in Calculus for Ojugbele Daniel

Question

Ascertain that (del)(r^n)=nr^n-2 vector r

Answer 1

For a function $f(r)$ , which depends solely on absolute value of radius-vector $\bold r$, the formula for the gradient is the following: $\nabla f(r) = \frac{\partial f(r)}{\partial r} \frac{\bold r}{r}$ (this can be shown via direct differentiation w.r.t components or $\bold r$). Hence, $\nabla (r^n) = n r^{n-1} \cdot \frac{\bold r}{r} = n r^{n-2} \bold {r}$.