Derivative of a sum of exponential, power, and logarithmic terms

Apply the sum/difference rule to differentiate term by term: $f'(x) = \frac{d}{dx}[2e^x] + \frac{d}{dx}[3x^2] - \frac{d}{dx}[\ln x]$. This breaks the problem into three simpler derivatives, each handled with a known rule.

Using the constant multiple rule, $\frac{d}{dx}[2e^x] = 2e^x$ and $\frac{d}{dx}[3x^2] = 3\cdot 2x = 6x$ by the power rule, while $\frac{d}{dx}[\ln x] = \frac{1}{x}$. Combining these gives $f'(x) = 2e^x + 6x - \frac{1}{x}$.

The term coming from the logarithm is subtracted. Since the original function subtracts the natural logarithm term, the difference rule keeps that minus sign when differentiating. This gives the negative one over x term in the final derivative.