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

Problem

d()/d(x)*cos(e^x)

Solution

1. Identify the outer function as cos(u) and the inner function as u=e^x

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 e^x with respect to x to get e^x

5. Multiply the results together and substitute u=e^x back into the expression.

Final Answer

d(cos(e^x))/d(x)=−e^x*sin(e^x)

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