Dx(e^(ln(cos(5x))) = ? Come on this is easy. Just what to see if there is someone with mathamatical knowlege out there. lol
2006-08-10 07:45:43 · 9 answers · asked by Dragonheart 2 in Science & Mathematics ➔ Mathematics
Dx(e^(ln(cos(5x))) = -5 sin 5x.
2006-08-10 07:50:29 · answer #1 · answered by Jay H 5 · 1⤊ 0⤋
I'm guessing that the Dx means 'derivative with respect to x' (which is more easily written d/dx)
So
e^(ln(cos(5x)) = cos(5x)
and
(d/dx)cos(5x) = -5sin(5x)
But note, this is *only* valid over the
domain -π/10 < x < π/10
(Unless you really *want* the full, complex valued function over the entire z-plane for -π/5 < x < π/5. But the expression for that one is kinda ghastly)
This is another example of how easy it is to screw the pooch in analysis. In the original function you have to take ln(cos(5x)) which is kewl as long as cos(5x)>0 since ln(0) is undefined and ln of a negative number is a complex value.
Doug
2006-08-10 08:00:24 · answer #2 · answered by doug_donaghue 7 · 1⤊ 1⤋
e^ln can simplify out, so its
dx (cos 5x) = -5 sin 5x
2006-08-10 07:52:06 · answer #3 · answered by lexie 6 · 1⤊ 0⤋
There are 3 positions, subsequently 3 slots. _ * _ * _ each and each stands for President, vice chairman, and Secretary respectively. you are able to pick between 5 human beings for President, so the 1st slot fee is 5 5 * _ * _ Now that one guy or woman is already President, that guy or woman will not be able to be chosen for the different place. So now for vice chairman, you have purely 4 options. 5 * 4 * _ as quickly as back, no it is easy to occupy 2 positions, so which you have 3 options for Secretary 5 * 4 * 3 = 60 = B
2016-11-04 07:24:53 · answer #4 · answered by Anonymous · 0⤊ 0⤋
Dx(e^(ln(cos(5x))))
= Dx (cos(5x))
= -sin(5x) * 5
2006-08-10 09:05:13 · answer #5 · answered by Kyrix 6 · 0⤊ 0⤋
e^ln(A) = A
so we have
dx cos(5x)
-5 sin(5x)
2006-08-10 07:50:42 · answer #6 · answered by polloloco.rb67 4 · 1⤊ 0⤋
You can't without knowing what x or the answer is.
2006-08-10 07:59:16 · answer #7 · answered by Anonymous · 0⤊ 1⤋
would they be in here at this time of day?
2006-08-10 07:51:38 · answer #8 · answered by cbmaclean 4 · 0⤊ 1⤋
-5 sin(5x) DUH!
2006-08-10 08:12:19 · answer #9 · answered by music_is 3 · 0⤊ 1⤋