Implicit Differentiation

Germylew

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May 6, 2015
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[h=1]Let f(x)=sin^2(x). Express the relationship between a small change in x and the corresponding change in f in form dy=f (x)dx? :confused::mad:[/h]
 
Let f(x)=sin^2(x). Express the relationship between a small change in x and the corresponding change in f in form dy=f (x)dx? :confused::mad:

I'm a little confused. Should this be
Let y = sin2(x). Express the relationship between a small change in x and the corresponding change in y in the form of dy = f(x) dx.
If not something like this, I'm not understanding the problem. The way it is written, as dy=f(x)dx, it is the first time y has shown up and, as I understand it, has nothing to do with the "corresponding change in f".

Possibly as a hint for the solution, you might consider the sum and difference formulas for trig functions. Specifically
cos(a+b) = cos(a) cos(b) - sin(a) sin(b)
and the corresponding formula when a=b in terms of sin2(a).
 
You've kinda confused me as well. If it helps we often use f(x) and y interchangeably, if that is what you were referring to.
 
Well, that was much easier to understand thanks! I'm obviously not good at "math-speak". So I should write it dy=2sin(x)cos(x)dx ?
 
Well, that was much easier to understand thanks! I'm obviously not good at "math-speak". So I should write it dy=2sin(x)cos(x)dx ?

Yes. Or possibly dy = f'(x) dx; f'(x) = 2 sin(x) cos(x).

To clarify what I meant, it appeared that you were saying f(x) [or y, if you prefer] was both sin2(x) and 2 sin(x) cos(x) when you wrote down the formulas the first time, so obviously you meant something else. What I was trying to say was that made no sense to me and maybe you meant that there was another function g(x) so that dy=g(x)dx or maybe y was different than f and you meant ... or ...
 
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