|Nov1-03, 06:31 PM||#1|
I am in math 50 (calc one) and i would greatly appreate it if someone could please show me how to solve these problems. I have the anwsers, but i can't figure out how to get them. thank you
In both problems i am need to find the derivative of the function,(we just learned the chain rule, so i am 'supposed to' use that to figure them out. But if you know a another way, great.
y=te^(-t^2) i normally know how to solve this problems but the t before the e is messing me up. the answer is e^(-t^2)(1-2t^2)
y=(z^(1/2)/e^z) the answer is e^-z/(2(z^(1/2))-(z^(1/2))e^-Z
thank you again for your help.
|Nov1-03, 07:17 PM||#2|
1. d/dx ex = ex
2. d/dx eg(x)= g'(x) eg(x) (this is an example of chain rule, if you need further explanation, please tell.)
I'll do the first question and the second one is similar to the first one.
f(t) = te(-t2)
f'(t) = t d/dt(e(-t2)) + e(-t2)d/dt (t)
= t*(-2t)* e(-t2) (use formula 2 above) + e(-t2)
|Nov2-03, 09:01 AM||#3|
K L Kam did a good job so I'll just content my self with pointing out, since bjon-07 said specifically that it was the "t before the e" that was giving him trouble: use the PRODUCT rule!
(fg)'= f g'+ f' g
KL Kam used it when he said
"f'(t) = t d/dt(e(-t2)) + e(-t2)d/dt (t)"
|Nov3-03, 05:04 PM||#4|
Thank you for your help. I was trying to solve the whole thing using only the chain rule ( i did not use the product rule).