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

Problem

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

Solution

1. Identify the outer function and the inner function to apply the chain rule.

2. Apply the chain rule to the outermost function cos(u) where u=cos(cos(x))

3. Differentiate the inner function cos(cos(x)) by applying the chain rule again.

4. Differentiate the innermost function cos(x)

5. Combine all the resulting derivatives.

6. Simplify the signs by noting that there are three negative signs from the three cosine derivatives.

Final Answer

d(cos(cos(cos(x))))/d(x)=−sin(cos(cos(x)))⋅sin(cos(x))⋅sin(x)

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