Differentiate Exponential 73219D

1. **State the problem:** We want to differentiate the function $$f(x) = 4e^{7x}$$ with respect to $$x$$. 2. **Recall the differentiation rule for exponential functions:** The derivative of $$e^{u(x)}$$ with respect to $$x$$ is $$e^{u(x)} \cdot u'(x)$$, where $$u(x)$$ is a function of $$x$$. 3. **Identify the inner function:** Here, $$u(x) = 7x$$, so its derivative is $$u'(x) = 7$$. 4. **Apply the chain rule:** $$\frac{d}{dx}4e^{7x} = 4 \cdot \frac{d}{dx}e^{7x} = 4 \cdot e^{7x} \cdot 7$$ 5. **Simplify the expression:** $$4 \cdot 7 \cdot e^{7x} = 28e^{7x}$$ **Final answer:** $$\frac{d}{dx}4e^{7x} = 28e^{7x}$$