1. **Stating the problem:** We need to find the derivative of the function $f(x) = 7\ln x + 2$. 2. **Recall the derivative rules:** - The derivative of $\ln x$ with respect to $x$ is $\frac{1}{x}$. - The derivative of a constant is 0. - The derivative of a constant multiplied by a function is the constant multiplied by the derivative of the function. 3. **Apply the derivative:** $$\frac{d}{dx}(7\ln x + 2) = 7 \cdot \frac{d}{dx}(\ln x) + \frac{d}{dx}(2)$$ 4. **Calculate each derivative:** $$= 7 \cdot \frac{1}{x} + 0$$ 5. **Simplify the expression:** $$= \frac{7}{x}$$ **Final answer:** The derivative of $7\ln x + 2$ is $$\frac{7}{x}$$.