Related Rates - Fast

[Lemonds]

Is there any way to do some of the more complicated related rates problems, such as ones with trig functions or logs, quickly? I can do them, but it takes me more time than I would like to use trying to solve them by hand. Thanks in advance.

[FabensMath]

Like which one, give a specific example, place the problem and answer on here and the others and me here will do our best to help.
BTW Welcome to the forum! :)

[Lemonds]

Thanks for your response! Honestly, the problem that sparked my question is #58 on the District 2 Math test. It reads, "A right traingle has a hypotenuse of length 10". If one of the acute angles is decreasing at the rate of 5 degrees per second, how fast is the area of the triangle decreasing when this acute angle is 30 degrees? (nearest tenth)" The answer is B) 2.2 in^2/sec.

I probably should of put this in the Math forum, but I've seen many more related rate problems on Calculator than I have on Math. I see how to get the answer, just take the derivative of .5*h^2*sinx*cosx (and remember it's in radians), but it just takes me so long to derive the function. Is there any way to put this into an 89 or something, or do I just have to get extremely fast at doing related rate problems?

[FabensMath]

[Lemonds]

I see! So since we only have one variable changing with respect to time, we can just plug the equation in to the good 'ole 89 and solve it, sweet! So what would happen if we had two or more variables changing with respect to time? For example,

"A 15 foot ladder is resting against the wall. The bottom is initially 10 feet away from the wall and is being pushed towards the wall at a rate of 1/4 ft/sec. How fast is the top of the ladder moving up the wall 12 seconds after we start pushing?"

Could the 89 do implicit differentiaion for two variables with respect to t, or is by hand the only way to go?

[88bobcat]

[Lemonds]

Hmm... I think I keep making all of these problems into multi-variable problems... Anyways, thanks for the help! I appreciate it!

[88bobcat]

[Lemonds]

That last explanation kind of throws me for a loop, but I get it. Thanks for your help!