need help studying for calc final

By the Pythagorean Thorem :

z^2 = x^2 + y^2           differentiate both dides with respect to time, t

2z dz / dt   = 2x dx/dt   + 2y dy/dt

z dz/ dt   =  x dx / dt  +  y dy/dt

And dx/dt  =  3dy/dt  .....so...

z dz / dt  =  x (3 dy / dt) + y dy /dt

We have a      5 - 12 - 13     right triangle.....so when  x = 12 and y = 5, z = 13

So

13 dz / dt  =  12 (3 dy / dt) + 5 (dy / dt)

13 (1)   =  36 dy / dt  + 5 dy /dt

13 =  (36 + 5) dy /dt

13 = 41 dy /dt

(13/41) = dy /dt

And  dx /dt  =  3(dy /dt)  =  3 (13/ 41)  =  39/41

Thanks to Guest for pointing out my earlier silly error....!!!

I think Cphill is right except the part where he says its a 12-5-17 triangle. If you use the pythagoreom theorem then z= 13

so dx/dt=39/41