# Derivatives of the Natural Exponential and logarithmic Functions

1. Oct 4, 2011

### josh_123

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. Oct 4, 2011

### SammyS

Staff Emeritus
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) ?

3. Oct 4, 2011

### 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.