# Four Differentiation Questions

• Feb 25th 2007, 09:19 AM
SportfreundeKeaneKent
Four Differentiation Questions
The first ones obviously simple, I'm just not sure about the answer to the last two.

• Feb 25th 2007, 09:39 AM
CaptainBlack
Quote:

Originally Posted by SportfreundeKeaneKent
The first ones obviously simple, I'm just not sure about the answer to the last two.

c) is just the quotient rule, but I don't use the quotient rule, so I will leave it for someone else to show you (I would do it
using the product rule myself).

e) g'(x) = 7/x -2 (3) e^(3x)

RonL
• Feb 26th 2007, 05:42 AM
Soroban
Hello, SportfreundeKeaneKent!

I'll try the third one . . .

. . . . . . . . . .(2x² - 5)^3
c) .g(x) . = . --------------
. . . . . . . . . . (x + 1)^4

. . . . . . . .(x + 1)^4 3(2x² - 5)²·4x - (2x² - 5)³·4(x + 1)³
g'(x) . = . -------------------------------------------------------
. . . . . . . . . . . . . . . . . . . .(x + 1)^8

. . . . . . .4(x + 1)³(2x² - 5)² [3x(x + 1) - (2x² - 5)]
Factor: . --------------------------------------------------
. . . . . . . . . . . . . . . . . (x + 1)^8

. . . . . .4(2x² - 5)²(x² + 3x + 5)
. . . = . -----------------------------
. . . . . . . . . . . (x + 1)^5

• Mar 16th 2007, 01:10 PM
SportfreundeKeaneKent
Is the answer to a.) y'= 18x^2-14x+4/x^1/3?

and the answer to b.) f'(x)=4-12x or 4(1-3x)?
• Mar 16th 2007, 01:22 PM
CaptainBlack
Quote:

Originally Posted by SportfreundeKeaneKent
The first ones obviously simple, I'm just not sure about the answer to the last two.

c): I will use the product rule, but you probably will want to use the
quotient rule:

dg/dx = 3 (2 x^2 - 5)^2 (4x) / (x+1)^4 + (2x^2-5)^3 (-4)/(x+1)^5

........= 4 (2 x^2-5)^2/(x+1)^4 [3x - (2x^2-5)/(x+1)]
RonL
• Mar 19th 2007, 01:32 PM
SportfreundeKeaneKent
Could someone verify the second one b.) ? My friend and I are getting different answers even though there does not appear to be anything wrong with the way that either of us are doing the question.

The answer which I got is 2sqrt(1-4x) - 4x-2/sqrt(1-4x)
• Mar 19th 2007, 01:41 PM
AfterShock
Quote:

Originally Posted by SportfreundeKeaneKent
Could someone verify the second one b.) ? My friend and I are getting different answers even though there does not appear to be anything wrong with the way that either of us are doing the question.

The answer which I got is 2sqrt(1-4x) - 4x-2/sqrt(1-4x)

b.) f(x) = (2x - 1)*(1 - 4x)^(1/2)

f'(x) = 2*(1 - 4x)^(1/2) + (2x - 1)*(1/2)*(1 - 4x)^(-1/2)*(-4)

I'll let you do the simplifying.
• Mar 19th 2007, 01:49 PM
AfterShock
Quote:

Originally Posted by SportfreundeKeaneKent
The answer which I got is 2sqrt(1-4x) - 4x-2/sqrt(1-4x)

Correct. Be careful with parentheses on here:

2*sqrt(1 - 4x) - (4x - 2)/(sqrt(1 - 4x))

• Mar 19th 2007, 02:02 PM
SportfreundeKeaneKent
Can I simplify that by finding the comon denominator to get this?:

-12/sqrt(1-4x)
• Mar 19th 2007, 03:07 PM
qbkr21
Re:
What program are you using to write the problem? Obviously it isn't Latex because the system is still down...:rolleyes:
• Mar 19th 2007, 07:26 PM
SportfreundeKeaneKent

I think that that one is right, not sure though.

And qbrk, I don't know how to use that program so...
• Mar 19th 2007, 10:56 PM
AfterShock
Quote:

Originally Posted by SportfreundeKeaneKent
Can I simplify that by finding the comon denominator to get this?:

-12/sqrt(1-4x)

No, but you can simplify it to:

(4 - 12x)/sqrt(1 - 4x)
• Mar 19th 2007, 10:57 PM
AfterShock
Quote:

Originally Posted by SportfreundeKeaneKent