Brief Calculus.

Question

Find dx/dt at x = -3 if y = -3x²-2 and dy/dt = -2.

dx/dt = ...................

Answer 1

This is a related rates problem. Let's record the given information...

x = -3

dy/dt = -2

y = -3x²-2

Taking the derivative of x and y with respect to t will generate dx/dt and dy/dt. It is like treating t as the independent variable with x and y as the dependent variables...

d/dt (y = -3x²-2) --> dy/dt = -6x * dx/dt ( This is the chain rule application )

Using the given information..

-2 = 6*(-3)*dx/dt

dx/dt = 1/9