Find the derivative of the function

  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.

    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.
  2. jcsd

  3. 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.

    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]
  4. HallsofIvy

    HallsofIvy 41,265
    Staff Emeritus
    Science Advisor

    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: Nov 3, 2003
  5. 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).
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