1. The problem is to find the derivative operator $\frac{d}{dx}$, which represents the process of differentiating a function with respect to $x$. 2. The derivative of a function $f(x)$ is defined as: $$\frac{d}{dx}f(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$$ This formula calculates the instantaneous rate of change of $f(x)$ at any point $x$. 3. Important rules for differentiation include: - The derivative of a constant is 0. - The power rule: $\frac{d}{dx} x^n = n x^{n-1}$. - The sum rule: $\frac{d}{dx} (f(x) + g(x)) = \frac{d}{dx} f(x) + \frac{d}{dx} g(x)$. - The product rule and quotient rule for products and quotients of functions. 4. Since the problem only states $\frac{d}{dx}$ without a specific function, it represents the differentiation operator itself, which is applied to functions to find their derivatives. Final answer: $\frac{d}{dx}$ is the differentiation operator with respect to $x$.