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

Problem

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

Solution

1. Identify the outer function and the inner function to apply the Chain Rule. The outer function is sin(u) and the inner function is u=cos(x)

2. Apply the Chain Rule, which states that the derivative of ƒ*(g(x)) is ƒ′*(g(x))⋅g(x)′

3. Differentiate the outer function sin(u) with respect to u which results in cos(u)

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

5. Multiply the results together and substitute u=cos(x) back into the expression.

6. Simplify the final expression by moving the negative sign to the front.

Final Answer

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

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