Question

If `y=x^3+2x` and `dx/dt=5`, how do you find `dy/dt` when `x=2` ?

Answer 1

By Implicit Differentiation,

`{dy}/{dt}=70`

By differentiating with respect to `t`,

`{dy}/{dt}=d/{dt}(x^3+2x)=(3x^2+2){dx}/{dt}`

by plugging in `x=2` and `{dx}/{dt}=5`,

`=[3(2)^2+2] (5)=70`