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

Sagot :

semsee45

Answer:

[tex]\dfrac{dy}{dt}=432[/tex]

Step-by-step explanation:

Differentiate [tex]y=4(x^2-4x)[/tex]:

[tex]\implies y=4x^2-16x[/tex]

[tex]\implies \dfrac{dy}{dx}=8x-16[/tex]

[tex]\textsf{Given}\quad\dfrac{dx}{dt}=9[/tex]

Therefore:

[tex]\begin{aligned}\dfrac{dy}{dt}&=\dfrac{dy}{dx} \times \dfrac{dx}{dt}\\\\\implies \dfrac{dy}{dt}& = (8x-16) \times 9\\\\& = 9(8x-16)\end{aligned}[/tex]

When [tex]x=8[/tex]:

[tex]\implies \dfrac{dy}{dt}=9(8(8)-16)[/tex]

[tex]\implies \dfrac{dy}{dt}=432[/tex]

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