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

Problem

d(tan(ex))/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=ex

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 sec2(u)

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

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

Final Answer

d(tan(ex))/d(x)=ex*sec2(ex)

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