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how do you differentiate
what method would you use. Thank you
Use the chain rule.
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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.
Why did the vector cross the road?
It wanted to be normal.
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can you show the method of the chain rule please? Thank you
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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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.
A logarithm is just a misspelled algorithm.
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Thank you!
so using your way..
of f(x) = sin^2x
f'(x) = 2sinxcosx
is it true that 2sinxcosx = sin2x ? and why?
thank you
To prove that you have to use the formula:
sin(A±B)=sinAcosB ± cosAsinB
then you make A=B=x
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how do you prove that though
The Beginning Of All Things To End.
The End Of All Things To Come.
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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)
Numbers are the essence of the Universe
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ah, never thought of trying that.
The Beginning Of All Things To End.
The End Of All Things To Come.
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