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#1 2007-04-20 05:53:06

entony
Guest

derivative

how do you differentiate

what method would you use. Thank you

#2 2007-04-20 06:17:50

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: derivative

Use the chain rule. smile

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#3 2007-04-20 07:49:37

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: derivative

Jane's method is the one that I'd probably use as well.

Other options are the product rule, or messing around with trig. identities to try to get something that's easier to differentiate.


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#4 2007-04-20 09:03:50

entony
Guest

Re: derivative

can you show the method of the chain rule please? Thank you

#5 2007-04-20 09:27:04

Zhylliolom
Real Member
Registered: 2005-09-05
Posts: 412

Re: derivative

Imagine that a mother function f(x) is pregnant with her baby function g(x). Then the mother function looks like f(g(x)). Then one day the mother function goes into labor, so at the hospital Doctor Derivative needs to differentiate her to help her give birth. First he differentiates the mother f(x), and then the baby g(x) comes out differentiated as well. The end result looks like this: f'(g(x))g'(x). This process is known as the chain rule.

In other words, (f(g(x)))' = f'(g(x))g'(x), or

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#6 2007-04-20 09:31:43

mikau
Member
Registered: 2005-08-22
Posts: 1,504

Re: derivative

in other words, the derivative of u^2 is equal to 2u du, note however, that u itself can be another function, and du would denote its derivative. Therefore, the derivative of f(x)^2 is equal to 2f(x) * f'(x)

This is whats known as the chain rule.

here, we have sin^2(x), if we let u = sin(x) than, du = cos(x) dx
the derivative of u^2 is 2u du, making the substitutions we get
2sin(x) cos(x) dx.


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#7 2007-04-20 21:44:23

entony
Guest

Re: derivative

Thank you!

#8 2007-04-20 21:47:53

entony
Guest

Re: derivative

so using your way..

of f(x) = sin^2x

f'(x) = 2sinxcosx

is it true that 2sinxcosx = sin2x ? and why?

thank you

#9 2007-04-21 09:36:09

freddogtgj
Member
Registered: 2006-12-02
Posts: 54

Re: derivative

To prove that you have to use the formula:
sin(A±B)=sinAcosB ± cosAsinB

then you make A=B=x

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#10 2007-04-21 09:53:56

luca-deltodesco
Member
Registered: 2006-05-05
Posts: 1,470

Re: derivative

how do you prove that though tongue


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#11 2007-04-21 11:27:09

Stanley_Marsh
Member
Registered: 2006-12-13
Posts: 345

Re: derivative

Use vectors~

To prove sin(A-B) , just let A( cosA, sinA) ,B(sinB , cosB)

Last edited by Stanley_Marsh (2007-04-21 11:27:40)


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#12 2007-04-21 18:24:10

luca-deltodesco
Member
Registered: 2006-05-05
Posts: 1,470

Re: derivative

ah, never thought of trying that. tongue


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