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

Problem

d(e^tan(x))/d(x)

Solution

1. Identify the outer function as e^u and the inner function as u=tan(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 tan(x) with respect to x which results in sec^2(x)

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

Final Answer

d(e^tan(x))/d(x)=e^tan(x)*sec^2(x)

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