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

Problem

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

Solution

1. Identify the outer function and the inner function to apply the Chain Rule. The outer function is tan(u) and the inner function is u=e^x

2. Apply the Chain Rule which states that (d(ƒ)*(g(x)))/d(x)=ƒ^′*(g(x))⋅g(x)^′

3. Differentiate the outer function with respect to its argument. The derivative of tan(u) is sec^2(u)

4. Differentiate the inner function with respect to x The derivative of e^x is e^x

5. Multiply the results together to find the final derivative.

Final Answer

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

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