Solution: ▽ · F = −3xy / (x2 + y2)^5/2

scholesmu · May 22, 2010

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

Solution: ▽ · F = −1 / (x2 + y2)^3/2

waht · May 22, 2010

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

HallsofIvy · May 23, 2010

scholesmu said:

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

Solution: ▽ · F = −1 / (x2 + y2)^3/2

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

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

Solution: ▽ · F = −3xy / (x2 + y2)^5/2

Discussion

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Solution: ▽ · F = −3xy / (x2 + y2)^5/2

Discussion

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