Question

If y = x^3 + 5 and dx/dt= -6, find dy/dt at x = -5.

Answer 1

`\sf\\\textsf{Use the chain rule.}\\\\(dy)/(dt)=(dy)/(dx)*(dx)/(dt)=(d(x^3+5))/(dx)*(-6)=(3x^2+0)*(-6)=-18x^2\\\\\textsf{At x = -5,}\\(dy)/(dt)=-18(-5)^2=-450`