Solve e^(2x)

Step-by-step solution

1. Identify the outer function $e^u$ and inner function $u = 2x$.

2. Derivative of $e^u$ with respect to $u$ is $e^u$ (the unique fixed-point function).

3. Derivative of inner $2x$ with respect to $x$ is $2$.

4. Apply the chain rule: $\frac{d}{dx}e^{2x} = e^{2x} \cdot 2 = 2e^{2x}$.