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I really do not understand how to do these problems, so many weird math tricks and rules and I am getting caught up on at least a dozen in this problem. Anyways I am supposed to find:

Each side of a square is increasing at a rate of $6 \text{ cm/s}$. At what rate is the area of the square increasing when the area of the square is $16 \text{ cm}^2$?

I think what I need to do is set it equal to 16 or 4, but I am not sure which so the problem will look like $4=s(36)$ but I am not sure what to do with that.

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    You are asked a length. What. Is. The. Length. At. Time t? Let me try once more to help you: you are given only two things, the length at time 0 (that is, 4 cm) and the rate of increase of the length (that is, 6 cm/s), right? Hence you have to use them and them only...2011-10-02

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We may define rate as $\frac{dP}{dt}$ , so let's find first derivative of the area formula $P=a^2$

$\frac{dP}{dt}=2a\frac{da}{dt}$ since $P=a^2 \Rightarrow a=\sqrt{P}$

$\frac{dP}{dt}=2\sqrt{P}\frac{da}{dt} \Rightarrow \frac{dP}{dt}=2*4*6 \frac{cm^2}{s} \Rightarrow \frac{dP}{dt}=48\frac{cm^2}{s}$

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    I know I get frustrated with math, but I have$a$ton of homework to do and this is one of the first problems I attempted and I wasn't even able to do any of them. That is beyond frustrating for me.2011-10-02
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pedja's answer does seem to be expressed in a somewhat complicated way.

Let $A$ be the area in square centimeters. Let $s$ be the length of the side in centimeters. Let $t$ be time in seconds.

Then we are given $\dfrac{ds}{dt} = 6$.

We recall that $A = s^2$.

We want $\dfrac{dA}{dt}$ when $A=16$.

$ \frac{dA}{dt} = \frac{d}{dt} s^2 = 2s \frac{ds}{dt}. $

When $A=16$ then $s=4$ and $ds/dt = 6$. So $ 2s\frac{ds}{dt} = 2\cdot4\cdot 6. $

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    Just for the record: I DID NOT put you down. The elementary questions I asked (if tackled one by one and in the right order) are the easiest way to reach the solution that I could think of. These are elementary BY DESIGN. You left deliberately (and without notification) this (carefully selected) path to the solution. The effect (apart from alienating people) is that you are back to square one of your frustration. But the path is still there, if and when you choose to forget all this nonsense of looking-like-an-idiot which worries you so much and just hinders your learning process...2011-10-07