Question

I am completely lost on this problem.
Assume x = x(t) and y = y(t). Find dx/dt if x^2(y-6) = 12y+3 and dy/dt = 2 when x=5 and y=12. Can you take me through this step by step?

Answer 1

It might be prudent to first try to find
\[\Large \frac{dx}{dy}\]
implicitly or otherwise :)

Answer 2

where do you start with the dx/dy, then?

Is it d/dx (2x) , d/dx (y-6) , and d/dx (12y-3) ??

Answer 3

Oh, you do it implicitly. At worst, you have to do this...
\[\Large x^2(y-6 )=12y-3\\\Large x^2=\frac{12y-3}{y-6}\\\\\\\\\\\Large x = \sqrt{\frac{12y-3}{y-6}}\]
And differentiate x with respect to y.

Answer 4

But I think implicit is nicer...