- #1

IslandHead

- 10

- 0

## Homework Statement

The electrical potential can be described by the following equation:V= 200/(x

^{2}+ y

^{2})

^{1/2}find dV when x=2 and y=1

## Homework Equations

n/a

## The Attempt at a Solution

dv/d(x,y) = ∂/∂x + ∂/∂y

=200/(x

^{2}+ y

^{2})

^{(1/2)}+200/(x

^{2}+ y

^{2})

^{(1/2)}

replace variables with C where necessary and rearrange for easy of deriving =200(x

^{2}+ C)

^{(1/2)}+200(C + y

^{2})

^{(1/2)}

Chain rule and exponent rule

=200(-1/2)(2x)(x

^{2}+ C)

^{(-3/2)}+200(-1/2)(2y)(C + y

^{2})

^{(-3/2)}

=-200x(x

^{2}+ C)

^{(-3/2)}+ -200y)(C + y

^{2})

^{(-3/2)}

=-200x(x

^{2}+ y

^{2}) )

^{(-3/2)}+ -200y)(x

^{2}+ y

^{2})

^{(-3/2)}

Then I plug in the values x=2 and y=1 and dV=-53.7 V/m, I'm not very confident with multivariable calculus and just wanted to check to see if this is right.I've never had to do this before, it is fir physics, not a math class