# How to find ▽ · F ?

1. May 22, 2010

### scholesmu

Find ▽ · F if F = x i / (x2 + y2)^3/2 + y j (x2 + y2)^3/2 .

Solution: ▽ · F = −1 / (x2 + y2)^3/2

2. May 22, 2010

### waht

Find the partial derivatives of F with respect to x, y and z and then add them up.

3. May 23, 2010

### HallsofIvy

The derivative of $x/(x^2+ y^2)^{3/2}= x(x^2+ y^2)^{-3/2}$ with respect to x, by the product rule, is $(x^2+ y^2)^{-3/2}- (3/2)(x)(2x)(x^2+ y^2)^{-5/2}$
$= (x^2+ y^2)(x^2+ y^2)^{-5/2}- 3x^2(x^2+ y^2)^{-5/2}$$= (y^2- 2x^2)/(x^2+ y^2)^{5/2}$.

Now, what is the derivative of $y/(x^2+ y^2)^{3/2}$?