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

Problem

d()/d(x)*etan(x)

Solution

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

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

3. Differentiate the inner function u=tan(x) with respect to x to get sec2(x)

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

Final Answer

d(etan(x))/d(x)=etan(x)*sec2(x)

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