Find the Derivative - d/dx cos(cos(x))

Problem

d(cos(cos(x)))/d(x)

Solution

1. Identify the outer function and the inner function to apply the Chain Rule.

2. Apply the Chain Rule, which states that (d(ƒ)*(g(x)))/d(x)=ƒ′*(g(x))⋅g(x)′

3. Differentiate the outer function cos(u) with respect to u where u=cos(x) which gives −sin(u)

4. Differentiate the inner function cos(x) with respect to x which gives −sin(x)

5. Multiply the results together: −sin(cos(x))⋅(−sin(x))

6. Simplify the signs, as the product of two negatives is a positive.

Final Answer

d(cos(cos(x)))/d(x)=sin(cos(x))*sin(x)

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