Thread: Four Differentiation Questions

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

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

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

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)?

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

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)

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.

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))

What answer did your friend get? They might be equivalent answers.

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

-12/sqrt(1-4x)

What program are you using to write the problem? Obviously it isn't Latex because the system is still down...

The other answer is 4-12x/sqrt1-4x

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

And qbrk, I don't know how to use that program so...

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)

Originally Posted by SportfreundeKeaneKent

The other answer is 4-12x/sqrt1-4x

Correct. These answers are equivalent.