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

Problem

d(ecos(x))/d(x)

Solution

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

2. Apply the chain rule, which states that d(eu)/d(x)=eu⋅d(u)/d(x)

3. Differentiate the inner function cos(x) with respect to x to get −sin(x)

4. Multiply the derivative of the outer function by the derivative of the inner function.

5. Simplify the expression by placing the negative sign and the trigonometric function at the front.

Final Answer

d(ecos(x))/d(x)=−sin(x)*ecos(x)

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