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.(adsbygoogle = window.adsbygoogle || []).push({});

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)=x^{2}e^{x}

6. (e^{x}(x^{2}-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=x^{7}(e^{x})-7x^{6}(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)

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!!!!

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# Derivatives of the Natural Exponential and logarithmic Functions

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