The discussion revolves around finding the derivative of the function f(x) = cos(sin(x)) using the chain rule. Participants are exploring the correct application of differentiation techniques and comparing their results with provided answer choices.
The conversation includes attempts to clarify the correctness of the derivative found and the relationship to the answer choices. One participant acknowledges a realization about the significance of the negative sign in multiplication, indicating a productive moment in the discussion.
Participants are working within the constraints of homework guidelines, which may limit the type of assistance they can receive. There is an emphasis on understanding the equivalence of different expressions rather than simply finding the correct answer.
Well, you're correct. What are the options given?Lion214 said:Homework Statement
Find the derivative of f when
f(x) = cos(sin(x))
The Attempt at a Solution
I used chain rule on this function, and came up with this;
-sin(sin(x)) times cos(x)
Now either I'm doing something completely wrong, or I'm not seeing what it is equivalent to in the answers choices online. I would appreciate some hints on how to go about this.
Mentallic said:Well, you're correct. What are the options given?
Lion214 said:1. f'(x) = -sin(x) cos(sin(x))
2. f'(x) = -cos(x) sin(sin(x))
3. f'(x) = sin(x) cos(cos (x))
4. f'(x) = -cos(x) sin(cos(x))
5. f'(x) = cos(x) sin(sin(x))
6. f'(x) = sin(x) cos(sin(x))
My feeling is that it's the first one, as it is the only one that has a negative sin, but I could be wrong and I'm not sure how could any of these be the same as my original answer.
Ray Vickson said:Why would you say that? You already gave 2) as your answer!