Ihave a question that involves derivatives in the context of a triangle. can someone confirm that the answer is 39/41?

X^2 + y^2 = z^2
d/dt[ x^2 + y^2 ] = d/dt[ z^2 ]
d/dt[ x^2 ] + d/dt[ y^2 ] = d/dt[ z^2 ]
2x*dx/dt + 2y*dy/dt = 2z*dz/dt
x*dx/dt + y*dy/dt = z*dz/dt
12*(3*dy/dt) + 5*dy/dt = z*1
12*(3*dy/dt) + 5*dy/dt = 13
12*(3*w) + 5*w = 13 ... letting w = dy/dt
36*w + 5*w = 13
41*w = 13
w = 13/41
dy/dt = 13/41
dx/dt = 3*(dy/dt)
dx/dt = 3*(13/41)
dx/dt = 39/41

You have the correct answer. Nice job.