Derivatives of the Natural Exponential and logarithmic Functions

[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:
(x^e)= x^e * lne*e= x^e* e=ex^e

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

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)-600e^x
dy/dx=(1-600e^x)/(2√x)

5. xe^x
dy/dx=xe^x (lnxe)(1)
dy/dx= xe^x(x)=x²e^x

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

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

8. (2e^x-1)/(5e^x+9)
dy/dx=(2e^x(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)

Homework Statement

Please tell me if any of my problems are wrong and how do I fix it?Thank you!

 

[SammyS]

There are really way too many questions for one post,

For #1, d/dx (x^e) is a trick question.

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

 

[Mark44]

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.