Finding dy/dt and dx/dt of f(x)

If x^2 + y^2 = 9, and dy/dt = -2, find dx/dt at the point (-1, 2)

a. 3
b. -3
c. 4
d. -4
e. 0.25

2x * dx/dt + 2y * dy/dt = 0
2*-1*dx/dt + 2*2*-2 = 0
-2 dx/dt - 8 = 0
dx/dt = 8/-2 = -4

This is your basic implicit differentiation problem.

First, you differentiate with respect to t. So you get

2x dx/dt + 2y dy/dt =0

Note that dx/dt and dy/dt are simply variables, like a or b.

Then you substitute your given values for dy/dt, x and y (note x= -1 and y = 2) and solve for the remaining variable, dx/dt.