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

1 Answer

5 votes

Answer:


(dy)/(dt) = - 4 cm/s

Explanation:

Let us revise the chain rule

If
(dy)/(dt) = a and
(dx)/(dt) = b, then


(dy)/(dx) =
(dy)/(dt) ÷
(dx)/(dt) =
(a)/(b)

∵ y = x² + 1

- Use the differentiation to find
(dy)/(dx)


(dy)/(dx) = 2x

∵ x = -1

- Substitute x by -1 in
(dy)/(dx)


(dy)/(dx) = 2(-1)


(dy)/(dx) = -2


(dy)/(dt) =
(dy)/(dx) ×
(dx)/(dt)


(dx)/(dt) = 2 cm/s


(dy)/(dt) = (-2) × (2)


(dy)/(dt) = - 4 cm/s

User Chris Neilsen
by
7.9k points

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