1. ## Implicit Differentiation Help

Problem statement:
Find dy/dt in terms of x, y, and dx/dt, assuming that x and y are differentiable functions of the variable t.

equation:
$x^3y^3 + y = 3$

So when I implicitly derive this equation, what do I chain on, and how would I find dy/dt? I think I am supposed to differentiate both sides of the equation with respect to t; but how would I go about doing this?

Thanks crew.

2. Originally Posted by r2d2
Problem statement:
Find dy/dt in terms of x, y, and dx/dt, assuming that x and y are differentiable functions of the variable t.

equation:
$x^3y^3 + y = 3$

So when I implicitly derive this equation, what do I chain on, and how would I find dy/dt? I think I am supposed to differentiate both sides of the equation with respect to t; but how would I go about doing this?

Thanks crew.
Yep, that's exactly what you do.

Think of x and y as x(t) and y(t). They are functions of t. So if you have something like x^2 and you want to take the derivative with respect to t, it would be 2x*(dx/dt). That's where the chain rule comes in.

Use the normal derivative rules like always, just remember to tack on the dx/dt or dy/dt when you differentiate x or y. Once you do that, just treat dy/dt like a normal variable and solve through algebra.