Derivative Exponential D558E8

1. **State the problem:** We want to find the derivative of the function $$f(x) = 3^x$$ with respect to $$x$$. 2. **Recall the formula:** The derivative of an exponential function $$a^x$$, where $$a$$ is a positive constant, is given by $$\frac{d}{dx} a^x = a^x \ln(a)$$. 3. **Apply the formula:** For $$f(x) = 3^x$$, the derivative is $$f'(x) = 3^x \ln(3)$$. 4. **Explain:** This means the rate of change of $$3^x$$ at any point $$x$$ is the value of $$3^x$$ multiplied by the natural logarithm of 3. 5. **Final answer:** $$\boxed{\frac{d}{dx} 3^x = 3^x \ln(3)}$$