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Derivatives of the Natural Exponential and logarithmic Functions

  1. Oct 4, 2011 #1
    1. Hello there, I have a few questions on the derivative homework that I did but not sure if it's right or not. These are difficult and my teacher doesn't go over all of them so I don't know if it is right or not. Please help me so I can understand the concepts before the upcoming test.

    1. Find dy/dx:
    (xe)= x^e * lne*e= xe* e=ex^e

    2. 5ex
    dy/dx=(5e^x)(ln5e)(1)=5e^x*5=25ex

    3. (e^x+x^10-1/x)
    dy/dx= e^x+10x^9-lnx

    4. √x-600e^x
    dy/dx=1/2(x-1/2)-600ex
    dy/dx=(1-600ex)/(2√x)

    5. xex
    dy/dx=xe^x (lnxe)(1)
    dy/dx= xex(x)=x2ex

    6. (ex(x2-7))
    dy/dx=e^x(x^2-7)+2x(ex)
    dy/dx=(x^2-1)e^x+2xe^x

    7. (e^x)/(x^7)
    [dy/dx=x7(ex)-7x6(ex)]/x^14

    8. (2ex-1)/(5ex+9)
    dy/dx=(2ex(ln2e)(5e^x+9)-(5e^x)(ln5e)(2e^x-1)/(5e^x+9)^2
    =(4e^x)(5e^x+9)-(25e^x)(2e^x-1)/(5e^x+9)^2
    --> distribution
    =(31e^x)/(5e^x+9)2

    9. (.5lnx-3x^25-2/x^3)
    =(.5/x)-(75x^24)+(6/x^4)

    10.[ (lnx)(x^5+10x^2-19)]
    1/x(x^5+10x^2-19)+(5x^4+20x)(lnx)
    simplify it I got [x^4+10x-19/x]+lnx(5x^4+20x)

    11. (lnx)/(x^20)
    dy/dx=1/x(x^20)-(20x^19)(lnx)/ (x^20)2
    simplify and I got [x^19-lnx(20x^19)]/ (x^40)
    1. The problem statement, all variables and given/known data



    Please tell me if any of my problems are wrong and how do I fix it?Thank you!!!!
     
  2. jcsd
  3. Oct 4, 2011 #2

    SammyS

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    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    There are really way too many questions for one post,

    For #1, d/dx (xe) is a trick question.

    e is just another number, like 3 or 7 or π ... What is d/dx (x5) ?
     
  4. Oct 4, 2011 #3

    Mark44

    Staff: Mentor

    I agree with Sammy -- too many questions in this post.

    Start a new post with at most 3 of the problems. If necessary, create additional posts with the other problems.
     
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