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

Problem

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

Solution

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

2. Apply the Chain Rule, which states that the derivative of e^ƒ(x) is e^ƒ(x)⋅d(ƒ(x))/d(x)

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

4. Multiply the derivative of the outer function by the derivative of the inner function to find the final result.

Final Answer

d(e^cos(x))/d(x)=−sin(x)*e^cos(x)

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