The length of a rectangle is increasing at a rate of 4 cm/s and its width is increasing at a rate of 9 cm/s. When the length is 9 cm and the width is 6 cm, how fast is the area of the rectangle increasing?
How do you solve this?

Question

The length of a rectangle is increasing at a rate of 4 cm/s and its width is increasing at a rate of 9 cm/s. When the length is 9 cm and the width is 6 cm, how fast is the area of the rectangle increasing?
How do you solve this?

mathstudent55 · Answer

Let the length = x, and the width = y.

$A = xy$

$\dfrac{dA}{dt} = \dfrac{d}{dt}(xy) $

Use the product rule to differentiate:

$ \dfrac{A}{dt} = x \dfrac{dy}{dt} + y \dfrac{dx}{dt} $

Now use x = 9 cm, y = 6 cm, dx/dt = 4 cm/s, and dy/dt = 9 cm/s.

agentnao · Answer

I feel so stupid asking that question now. I tried writing that out myself, but for some reason, I ended up with way many more variables...maybe I just need to slow down and read things more closely before asking dumb questions. Thank you so much though,

mathstudent55 · Answer

Your question was not dumb at all. OS's purpose is exactly to ask questions. I just hope I was able to help you by steering you in the right direction.