Differentiating with respect to t implicitly

[marcuss]

a particle moves along the curve xy=10, x=2 and dy/dt=3, what is the value of dx/dt?


i tried product rule and got x*y*dy/dt + y*x*dx/dt = 0 and the answer that i get doesn't appear on the multiple choice answers
a)-5/2 b)-6/5 c) 0 d) 4/5 e) 6/5

i don't know what I am doing wrong a little help would be nice ty.

 

[Cyosis]

You did your differentiation wrong. Applying the product rule correctly yields d(xy)/dt=x dy/dt+y dx/dt.