Question

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

Answer 1

`(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