Finding dy/dt with equation and dy/dx

[GreatEscapist]

Homework Statement

If tan y + (x^3) = (y^2) + 1, and dx/dt = -2, what is the value of dy/dt at the point (1,0)?

Homework Equations

See above.

The Attempt at a Solution

I know I can't plug in my points until I get the equation... Do I just use implicit differentiation, then whenever I have a dx/dt plug in -2, and solve for the dy/dt? Or do I have to do something totally different?

 

[HallsofIvy]

Yes, differentiating with respect to t gives
$$sec^2(y) (dy/dt)+ 3x^2 (dx/dt)= 2y (dy/dt)$$

Put in the given values and solve for dy/dt.

 

[GreatEscapist]

That's what I thought! Thanks!