Partial derivatives are giving me the runs

[K.I.L.E.R]

So now that I'm doing my computational methods class I feel like going back to some old problems and solving them in different ways because I have way too much time on my hands and because it's fun.

Sphere intersection stuff involves quadratics, yada yada yada...

Anyway:

p0^2 + 2*p0*d + d^2 - r^2

Assume r^2 = constant. Derivative of a constant is 0.

simplifies eqtn to:
p0^2 + 2*p0*d + d^2

Break down the eqtn component wise:
x0 ^2 + 2*x0*xd + xd^2

dt/dx0 = 2*x0 + 2xD
dt/dxd = 2*x0 + 2*xd

the equations are a function of t because t is the value in the parametric equation where the intersections occur.

Do I now stick these derivatives together?
What the hell do I do now?

I need to do the same thing to the y and z components.
Surely there is a simpler way to take derivatives of parametric equations?

This is what happens when schools cancel maths subjects.

 

[standing ovation]

*sigh* If you only knew how trivial these sorts of questions were, being a mere application of mathematics and not a proof of it, you probably wouldn't ask them -- that's the vibe you get from physicists and mathematicians.

But I'm different. I will tell you the answer: it's in the back of the book!

 

[K.I.L.E.R]

There is no book.
That's the problem.

 

[CMAN]

You don't put them back together. A partial derivative is just that...partial. It's just giving you information in relation to the particular variable you derived in relation to.