find the gradient of 0=(sin sqrt(x^2 + z^2))/(x^2 + z^2)-y

[butterysteez]

I'm just messing around with some computer graphics and I got a little over my head in the math. I need to find the normal to this plane which I'm using to model water splashes.

 

0=(sin sqrt(x^2 + z^2))/(x^2 + z^2)-y

[Tom Mattson]

Do the partial derivatives one at a time. You wrote this as a quotient, but I like to rearrange complicated functions so that I never have to use the quotient rule, like so:

 

f(x,y,z)=(sin((x²+z²)^1/2))(x²+z²-y)^-1

 

f_x=(cos((x²+z²)^1/2))(1/2)(x²+z²)^-1/2(2x)(x²+z²-y)^-1+(sin((x²+z²)^1/2))(-1)(x²+z²-y)^-2(2x)

f_x=xcos(((x²+z²)^1/2))*(x²+z²)^-1/2*(x²+z²-y)^-1-2xsin(((x²+z²)^1/2))*(x²+z²-y)^-2

 

Happily, x and z occur symmetrically in this function, so you can find f_z by simply swapping x<-->z in the above derivative.

 

Finally,

 

f_y=sin((x²+z²)^1/2)(x²+z²-y)^-2

 

Tom

[butterysteez]

thanks a bunch man. do you want me to email you the program or the source?