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

Problem

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

Solution

1. Identify the outer function as cos(u) and the inner function as u=ex

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

3. Differentiate the outer function cos(u) with respect to u to get −sin(u)

4. Differentiate the inner function ex with respect to x to get ex

5. Multiply the results together and substitute u=ex back into the expression.

Final Answer

d(cos(ex))/d(x)=−ex*sin(ex)

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