Question

If DX/DT= 2cm/s x=-1 y=x^2+1 DY/DT=??

Answer 1

Answer:

$\frac{dy}{dt}$ = - 4 cm/s

Step-by-step explanation:

Let us revise the chain rule

If $\frac{dy}{dt}$ = a and $\frac{dx}{dt}$ = b, then

$\frac{dy}{dx}$ = $\frac{dy}{dt}$ ÷  $\frac{dx}{dt}$ = $\frac{a}{b}$

∵ y = x² + 1

- Use the differentiation to find $\frac{dy}{dx}$

∴ $\frac{dy}{dx}$ = 2x

∵ x = -1

- Substitute x by -1 in  $\frac{dy}{dx}$

∴  $\frac{dy}{dx}$ = 2(-1)

∴  $\frac{dy}{dx}$ = -2

∵  $\frac{dy}{dt}$ =  $\frac{dy}{dx}$ ×  $\frac{dx}{dt}$

∵ $\frac{dx}{dt}$ = 2 cm/s

∴  $\frac{dy}{dt}$ = (-2) × (2)

∴ $\frac{dy}{dt}$ = - 4 cm/s