Answer:
[tex]\frac{dy}{dt}[/tex] = - 4 cm/s
Step-by-step explanation:
Let us revise the chain rule
If [tex]\frac{dy}{dt}[/tex] = a and [tex]\frac{dx}{dt}[/tex] = b, then
[tex]\frac{dy}{dx}[/tex] = [tex]\frac{dy}{dt}[/tex] ÷ [tex]\frac{dx}{dt}[/tex] = [tex]\frac{a}{b}[/tex]
∵ y = x² + 1
- Use the differentiation to find [tex]\frac{dy}{dx}[/tex]
∴ [tex]\frac{dy}{dx}[/tex] = 2x
∵ x = -1
- Substitute x by -1 in [tex]\frac{dy}{dx}[/tex]
∴ [tex]\frac{dy}{dx}[/tex] = 2(-1)
∴ [tex]\frac{dy}{dx}[/tex] = -2
∵ [tex]\frac{dy}{dt}[/tex] = [tex]\frac{dy}{dx}[/tex] × [tex]\frac{dx}{dt}[/tex]
∵ [tex]\frac{dx}{dt}[/tex] = 2 cm/s
∴ [tex]\frac{dy}{dt}[/tex] = (-2) × (2)
∴ [tex]\frac{dy}{dt}[/tex] = - 4 cm/s
