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

Problem

d(esec(x))/d(x)

Solution

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

2. Apply the chain rule, which states that the derivative of eƒ(x) is eƒ(x)⋅d(ƒ(x))/d(x)

3. Differentiate the inner function sec(x) to get sec(x)*tan(x)

4. Multiply the results to find the final derivative.

Final Answer

d(esec(x))/d(x)=esec(x)*sec(x)*tan(x)

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