Question

If y=-2x^(3)-3x, determine dy/dt when x=1 and dx/dt=4

dy/dt=?

Answer 1

Here we differentiated bothparts of equation, knowing that f(x(t))'=f'(x(t))*x'(t), then we simply put the
values of x and x'(t) into the obtained expression:
dy/dt=-6x^2(dx/dt)-3dx/dt=-24-12=-36