Derivative of f(x) = cos(sin(x)) using chain rule

[Lion214]

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]

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.

Well, you're correct. What are the options given?

 

[Lion214]

Well, you're correct. What are the options given?

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]

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.

Why would you say that? You already gave 2) as your answer!

 

[Lion214]

Why would you say that? You already gave 2) as your answer!

Ack! I just realized that it doesn't matter where the negative sign is if there's only multiplication! I feel silly. Thanks for answering for allowing me to see this!