Question

Consider the following equation.
y = 4(x2 – 4x)
Find dy/dt, given x = 8, dx/dt = 9.

Answer 1

`(dy)/(dt)=432`

Explanation:

Differentiate
`y=4(x^2-4x)`:

`\implies y=4x^2-16x`

`\implies (dy)/(dx)=8x-16`

`\textsf{Given}\quad(dx)/(dt)=9`

Therefore:

`\begin{aligned}(dy)/(dt)&=(dy)/(dx) * (dx)/(dt)\\\\\implies (dy)/(dt)& = (8x-16) * 9\\\\& = 9(8x-16)\end{aligned}`

When
`x=8`:

`\implies (dy)/(dt)=9(8(8)-16)`

`\implies (dy)/(dt)=432`