The derivative of the function f(x) = cos(sin(x)) is calculated using the chain rule. The correct derivative is f'(x) = -sin(sin(x)) * cos(x), which corresponds to option 1 from the provided choices. The confusion arose from the placement of the negative sign, which does not affect the multiplication of terms. This highlights the importance of understanding the chain rule in calculus for differentiating composite functions.
PREREQUISITESStudents studying calculus, particularly those focusing on differentiation techniques, and educators looking for examples of applying the chain rule in real problems.
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!