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

User CJCombrink
by
8.2k points

1 Answer

8 votes

Answer:


(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

User Magomar
by
8.4k points

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