Log Questions (1 Viewer)

[allGenreGamer]

One test after another... my test on logs is on next tuesday. Please help me with some questions:

1) Differentiate:
(e^x - e^-x)/(e^3x + e^-3x)
Answer: (1 - ln x^2)/x^2

2) Integrate (x^-2)(e^(1/x))
Answer: -e^(1/x) + C

3) Differentiate 10^(x^1/2)
Answer: (10^(x^1/2) . ln10)/ 2x^(1/2)

4) Change the subject to x in y=e(2x)

Please provide me with slight explanation for these questions. Thanks in advance!

 

[kpq_sniper017]

Originally posted by allGenreGamer
One test after another... my test on logs is on next tuesday. Please help me with some questions:

1) Differentiate:
(e^x - e^-x)/(e^3x + e^-3x)
Answer: (1 - ln x^2)/x^2

2) Integrate (x^-2)(e^(1/x))
Answer: -e^(1/x) + C

3) Differentiate 10^(x^1/2)
Answer: (10^(x^1/2) . ln10)/ 2x^(1/2)

4) Change the subject to x in y=e(2x)

Please provide me with slight explanation for these questions. Thanks in advance!

4) Take the log to base e of both sides.

Edit: provided that was y=e^2x

 

[govich]

Originally posted by allGenreGamer
2) Integrate (x^-2)(e^(1/x))
Answer: -e^(1/x) + C

remember 1/x = x^-1
here you can let u = x^-1
so du/dx = -x^-2
etc etc..

Originally posted by allGenreGamer
3) Differentiate 10^(x^1/2)
Answer: (10^(x^1/2) . ln10)/ 2x^(1/2)

d/dx a^x = (ln a).a^x

so for this question just use that and then chain rule..

 

[CrashOveride]

For the first one, i'm not sure about their answer, or maybe u mistyped something. Because i did it manually, and my answer matches with that from calc101.com

If you go to calc101.com putting your question in there yields:

actually its a bit long and messy but yeah just go there and check it out =p