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SSC Applied Mathematics QUESTION #4135
Question 1
Given $\nabla r^n = nr^{n-2}\vec{r}$, what is $\nabla \left(\frac{1}{r}\right)$ for $r \neq 0$?
  • $-\frac{\vec{r}}{r^3}$✔️
  • $\frac{\vec{r}}{r^3}$
  • $-\frac{1}{r^2}$
  • $\frac{1}{r^2}$
Correct Answer Explanation
Using formula with $n = -1$: $\nabla r^{-1} = (-1)r^{-3}\vec{r} = -\frac{\vec{r}}{r^3}$.