# rate of change of an area

• May 11th 2008, 03:49 PM
ikickyouindanuts
rate of change of an area
I am asked to find the rate of change of the area of a rectangle, given it's length is 15 ft, and increasing at 3 ft/sec, and it's width is 6 ft, increasing at 2 ft/sec.

Rate of change of the area (dA) should just be the product of the other two rates (dx*dy) right? or am I missing something? Please help.
• May 11th 2008, 04:26 PM
galactus
The area is given by A=LW

Therefore, by the product rule: $\frac{dA}{dt}=L\frac{dW}{dt}+W\frac{dL}{dt}$

$\frac{dA}{dt}=15(2)+6(3)=48$
• May 12th 2008, 07:38 PM
ikickyouindanuts
hmmm... I am unfamiliar with this rule. Or at least, I may need a refresher to remember it.