1. The problem is to find the derivative of the function $y = e^{ax}$ where $a$ is a constant. 2. According to the derivative formula for exponential functions, the derivative of $e^{ax}$ with respect to $x$ is given by: $$\frac{d}{dx} e^{ax} = a e^{ax}$$ 3. This formula comes from the chain rule, where the outer function is $e^u$ and the inner function is $u = ax$. 4. Applying the chain rule, we differentiate the outer function $e^u$ to get $e^u$ and multiply by the derivative of the inner function $ax$, which is $a$. 5. Therefore, the derivative is: $$\frac{d}{dx} e^{ax} = a e^{ax}$$ 6. This means the rate of change of $e^{ax}$ with respect to $x$ is proportional to the function itself, scaled by the constant $a$. Final answer: $$\frac{d}{dx} e^{ax} = a e^{ax}$$