Find the Derivative - d/d@VAR f(x)=e^(cos(x))

Problem

d(e^cos(x))/d(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 d(e^u)/d(x)=e^u⋅d(u)/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.

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

Final Answer

d(e^cos(x))/d(x)=−sin(x)*e^cos(x)

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