Math - Derivatives

I find it difficult to take the derivative of something that has a constant base with a variable as an exponent...and simplify it... PLEASE HELP ME!

f(x) = e^(x^(-1))

f'(x) = -1(e^(x^(-2))e^(x^(-1))

f'(x) = -e^(x^(-2))e^(x^(-1))

?????

and... f(x) = 3^x

f'(x) = 3^x

asked by Anonymous
  1. d/dx e^u = e^u du/dx
    here u = x^-1
    du/dx = -1 x^-2
    so
    d/dx e^(x^-1) = -x^-2 e^(x^-1)
    = -(1/x^2)e^(1/x^2)
    Try the others using that recipe:
    d/dx e^u = e^u du/dx

    posted by Damon
  2. WOW that actually helps a lot and less confusing to solve! Thanks so much!

    posted by Anonymous

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus--> bobpursley

    How do you get m=0? from taking the second derivative? does c=1? Can you check my work on how I get the derivative of R=M^2(c/2-m/3) NEXT R=1/2(CM^2)-1/3(M^3) NEXT dR/dM=CM-M^2. I checked in the back, and that was the answer for
  2. calculus

    Please help with this. I need the first derivative of f(x)=4(x+squareroot (x(8-x)) and then the second derivative of this to show by the second derivative test that it is a local maximum. This is difficult to put into form here
  3. math derivative please help

    the derivative of 2x^e is zero right or no? do i have to use the log formula 2 x^e is x to the power 2.718.. It is not a constant and therefore the derivative is not zero. Use the formula for the derivative of x to a power that is
  4. Calculus

    R=M^2(c/2-m/3) dR/dM=CM-M^2 I found the derivative. Now how would I find the vale of M that maximize the derivative dR/dM? set it to zero, and solve for m. You get two solutions. Use the second derivative to see which one is the
  5. calculus

    Please help with this. I submitted it below and was asked to clarify by Henry (hope this is clearer and thank you). I need the first derivative of f(x)=4(x+ sqrt (x(8-x)).And then the second derivative of this to show by the
  6. calculus

    Please help with this. I submitted it below but no one responded. I need the first derivative of f(x)=4(x+ then the square root to include (x(8-x)), then close bracket.And then the second derivative of this to show by the second
  7. Quantum mechanics, eigenfunctions!

    Determine if the function sin(x)*e^(ax) where a=constant is an eigenfunction of the operators d/dx and d^2/(dx)^2 Okay. My understanding is that you use the operator and perform its "thing" on the function. In this case, you will
  8. Calc Help

    Find two functions that this could be the derivative of: y'=4x+7 I have one: y=2x^2 + 7x I cant think of another one!! add a constant. Remember that you can add an arbitrary constant to any integral. The derivative will be the
  9. calc

    derivative of (x^3/6)+(1/2x)? i got (x^2/2)-(1/2x^2) is that correct? and then wut is the (F'(x))2?...meaning the derivative squred? if you meant (1/2)x^2 - 1/(2x^2) you are correct I don't think they are looking for the square of
  10. Calc Help

    Find two functions that this could be the derivative of: y'=4x+7 Remember the derivative of any constant is zero. take its antiderivative i suppose... y= 2x^2 + 7x + any number

More Similar Questions