#1
my math professor is a douchenozzle and doesnt know how to count, long story short, she sucks at teaching. so i need help with this homework shit and nobody to help, so what is the derivative of f(x)=cos(3x)sin(2x)
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#2
I'm a little rusty on my calculus...

f ' ( x ) = - 3 sin ( 3 x ) sin ( 2 x ) + 2 cos ( 3 x ) cos ( 2 x )

EDIT : In all fairness, vintage said it first
Last edited by NoBC14 at Oct 12, 2008,
#3
dont call me a douchenozzle...you see me after class!
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#4
okayyy product rule!
U = cos(3x)
U' = -3sin(3x)
V = sin(2x)
V' = 2cos(2x)

so, since f'(x) = u'v + uv'
f'(x) = -3sin(3x)sin(2x) + 2cos(3x)cos(2x)
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#5
Well first work out the cos of 3 X x. Then the sin of 2 X x. Then times them together.

Voila.
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#6
Quote by vintage x metal
okayyy product rule!
U = cos(3x)
U' = -3sin(3x)
V = sin(2x)
V' = 2cos(2x)

so, since f'(x) = u'v + uv'
f'(x) = -3sin(3x)sin(2x) + 2cos(3x)cos(2x)


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#7
Quote by vintage x metal
okayyy product rule!
U = cos(3x)
U' = -3sin(3x)
V = sin(2x)
V' = 2cos(2x)

so, since f'(x) = u'v + uv'
f'(x) = -3sin(3x)sin(2x) + 2cos(3x)cos(2x)

ya i understand all that, but i dont see where you got the 3 and 2 coefficients in the u' and v', unless it is some trick i havent learned yet or there is some other double angle function i am forgetting.
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Last edited by shadowsoldier08 at Oct 12, 2008,
#8
you have to take the derivative of the 2x and 3x inside the sin/cos functions
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#9
Quote by shadowsoldier08
ya i understand all that, but i dont see where you got the 3 and 2 coefficients in the u' and v', unless it is some trick i havent learned yet or there is some other double angle function i am forgetting.


It's the Chain Rule

y = f ( g ( x ) )

y ' = f ' (g ( x ) ) * g '

( * - multiplied by... )
Last edited by NoBC14 at Oct 12, 2008,
#10
ahhhhh nvm, i tried to combine the (3x) and (2x) sin/cos and i got like sin^2(6x) or someting, cuz i never can tell when im done reducing or not

thx very much
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#11
Quote by shadowsoldier08
ya i understand all that, but i dont see where you got the 3 and 2 coefficients in the u' and v', unless it is some trick i havent learned yet or there is some other double angle function i am forgetting.

Nah, it's the chain rule. Chain rule specifies that not only do you do the derivative of the entire trig function, but also the expression inside of the parentheses. For instance:
f(x) = sin(x^2)
f'(x) = cos(x^2)[the derivative of the trig expression] * 2x[the derivative of the expression inside of the parentheses)
ultimately giving you:
f'(x) = 2xcos(x^2)
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#12
I'm a freshman in Geometry Honors and my brain just busted.
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#13
Sorry for the sh!tty contribution but i just wanna say i wish i knew how to do all this stuff!! It looks so confusing/interesting and i suck at maths so i guess its never gunna happen...
#14
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Sorry for the sh!tty contribution but i just wanna say i wish i knew how to do all this stuff!! It looks so confusing/interesting and i suck at maths so i guess its never gunna happen...

Calculus is a hell of a lot of fun and not difficult at all; it just takes some getting used to.
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#15
Quote by shadowsoldier08
doesnt know how to count

so what is the derivative of f(x)=cos(3x)sin(2x)

SHE doesn't know how to count, and YOU'RE asking for advice on a forum
#16
Dont worry, I took advanced calculus I and II in high school as a senior. Only about 30 people out of my school of 2000 students take those classes a year.

What I'm saying is, you'll catch up if math is your thing.

And like Vintage X Metal said, Calculus isnt that hard, it just requires a different way of thinking.
#17
yeah i agree, and pardon me in case of flaming, but i dont see hwo the hell calc is going to help me if i plan to be a something like a pharmacist, unless i just havnt had the class long enough to understand its full 'use'
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#18
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SHE doesn't know how to count, and YOU'RE asking for advice on a forum

HE was exaggerating, and YOU'RE a dickhead.
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#19
Quote by shadowsoldier08
yeah i agree, and pardon me in case of flaming, but i dont see hwo the hell calc is going to help me if i plan to be a something like a pharmacist, unless i just havnt had the class long enough to understand its full 'use'


You can apply calculus to pretty much anything you want to. I dont know anything about being a pharmacist, but I'm sure it could have its applications, even if they are vague and somewhat pointless.
#20
Quote by shadowsoldier08
yeah i agree, and pardon me in case of flaming, but i dont see hwo the hell calc is going to help me if i plan to be a something like a pharmacist, unless i just havnt had the class long enough to understand its full 'use'

I dunno about you, but to be able to find an actual answer to something in a world with so many open loops is, in itself, satisfying.
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