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

Problem

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

Solution

1. Identify the outer function and the inner function to apply the Chain Rule. The outer function is e^u where 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 e^u with respect to u which results in e^u

4. Differentiate the inner function e^x with respect to x which results in e^x

5. Multiply the results together and substitute u=e^x back into the expression.

6. Simplify the expression using the laws of exponents if necessary, though leaving it in product form is standard.

Final Answer

d(e^(e^x))/d(x)=e^(e^x)*e^x

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