Find the derivative of the function

bjon-07

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.

problem one

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)

second problem

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.

KLscilevothma

Originally posted by bjon-07
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.

problem one

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)

The following two formulae are useful

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.

Let
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)

= e-t2[1-2t2]

HallsofIvy

Homework Helper
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)"

Last edited by a moderator:

bjon-07

Thank you for your help

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).

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving