Posted by Marissa on Tuesday, August 26, 2008 at 11:44pm.
Can somebody please check these over for me? I really want to know what I did wrong if I made mistakes!
Differentiate the following:
1. y = ln [(4-x)/(4+x)]
Since it's the ln of the entire thing, then I can apply ln a - ln b
so, dy/dx = y' = 1/(4-x) *(-1) - 1/(4+x) *(1)
dy/dx = y' = -1/(4-x) - 1/(4+x)
2. y = ln √((3u+2)/(3u-2))
so that's the same as
y = ln ((3u+2)/(3u-2))^(1/2)
= 1/2 ln ((3u+2/3u-2))
using the ln a - ln b property again:
1/2[ln(3u+2) - ln(3u-2)]
dy/dx = 1/2 [1/(3u+2)*3 - 1/(3u-2)*3]
dy/dx = 1/2[3/(3u+2) - 3/(3u-2)
3. y = f(x) = tan(ln(4x+1))
so first I found the derivative of ln 4x+1
= 1/(4x+1)*4 = 4/(4x+1)
I plugged that number back into the original, making it
y = f(x) = tan(4/(4x+1))
Since the d/dx of tan x = sec^2x,
does it just end up being
dy/dx = sec^2(4/(4x+1)) ?
I am confused on how to do a problem like this:
4. f(t) = ln (2t+1)^3/(3t-1)^4
I can't apply the ln a - ln b property since it's not the ln of the entire thing, so how should I do it?
Answer this Question
- Math(please check) - 1) Differentiate the following: a) y=(x^3+5x)^6 (x^2+1)^7 (...
- Calculus - How do you use imlicit differentiation to differentiate e^(xy)? I ...
- Differentiate - Can someone please differentiate y = sin x / x for me? What I ...
- Please check Algebra - Please take a look at my work and let me know if I made ...
- Math - Can someone please check my answers below for accurateness? The ...
- Algebra - Hiya. I have 7 expressions that I have been asked to simplify. I ...
- English - Can you please check the following sentences? I had left them out. ...
- Differentiation - Differentiate the following (1) 12x^3 - 6x - 2 (2) 1/4x^4 - 2x...
- Math...Algebra :S - Hi, okay um. I'm trying to get his math question (Algebra :o...
- English - 1. They made a mistake. 2. They made two mistakes in composition. 3. ...