Question

I'm having to take the derivative of the following...can someone help me with if for a medal?

Answer 1

\[L^2=(\frac{-6x}{x-4})^2+x^2\]

Answer 2

I can see that you'd probably be better off squaring the fraction out, then combining it with the x^2 to have L^2 = fraction, then using the quotient rule and diving both sides by two to get dL/dx. What do you think?

Answer 3

Let me see if I'm understanding you correctly...

Answer 4

\[L2=(\frac{−6x}{x−4})^2+x^2\]\[L^2=\frac{36x^2}{\left(4-x\right)^2}+x^2\]\[L^2=\frac{x^4+52x^2-8x^3}{\left(x-4\right)^2}\]
Is that what you mean?

Answer 5

Yep. you should also multiply out the denominator (bottom) of the fraction. Then use quotient rule.

Answer 6

\[\frac{x^4+52x^2-8x^3}{x^2-8x+16}\]\[\frac{(4x^3-24x^2+104x)(x^2-8x+16)-(x^4-8x^3+52x^2)(2x-8)}{(x^2-8x+16)^2}\]\[\frac{(4x^5+360x^3+1664x-56x^4-1216x^2)-(2x^5+168x^3-24x^4-416x^2)}{(x^2-8x+16)^2}\]

Answer 7

you prolly don't need to xpand all that stuff out. though there's no harm in it.

what is the actual question? is \(L = L(x)\)?

Answer 8

Oh I generally just type it out in case I did something wrong. It makes it easier for the person helping me to identify where I went wrong (since I may not be able to see where).

And possibly? I don't really know.

Answer 9

This is just a part of a word problem I have. I keep getting one answer for my derivative, and the provided solution has something else written. I'm just trying to see what I'm doing wrong. The solution's answer is...\[2x+(\frac{72x}{x-4})[\frac{-4(72)}{(x-4)^2}]\]

Answer 10

@cathyangs
I can show you the solution if that would help?

Answer 11

So far I only have that you get 2x from simplifying what you've done so far, since 4x5 - 2x5 = 2x5, over x4 from the x2 squared is 2x. That might help. I think this problem is just a lot of algebra simplification from here on.

Answer 12

I'm sort of confused by some of your response, but I guess I'll just continue to simplify like you said.

Answer 13

Sorry I meant if you have the solution work that might help? But I do think your work will properly simplfy to the solution they gave you.

Answer 14

Yeah. When I solve for the derivative I can tell that I'm close since I get
\[2x+\frac{−72x^2}{(x−4)^3}+\frac{72x}{(x−4)^2}\]
and they get what I posted earlier. I'm just not sure why I'm getting a different answer no matter how many times I solve this.

Answer 15

Hm, those seem really close. Could it be that their answer is wrong, then? I think your work is right, its just simplifying. Maybe check again that all your terms are simplifying by the right terms of the same power?
Other than that, I'm not sure what else it could be.

Answer 16

I'll do that then. I can't tell if they're just writing it differently than I am or what, but I'll just keep doing what I am currently.
Thanks for your help.