1. The problem is to find the 1st and 2nd derivatives of a function. 2. Since the function is not given, let's consider a general function $f(x)$. 3. The 1st derivative of $f(x)$, denoted $f'(x)$ or $\frac{df}{dx}$, represents the rate of change or slope of the function. 4. The 2nd derivative, denoted $f''(x)$ or $\frac{d^2f}{dx^2}$, represents the rate of change of the 1st derivative, i.e., the curvature or concavity of the function. 5. For a specific example, if $f(x) = x^3$, then: - 1st derivative: $$f'(x) = \frac{d}{dx} x^3 = 3x^2$$ - 2nd derivative: $$f''(x) = \frac{d}{dx} 3x^2 = 6x$$ 6. Hence, the first and second derivatives of $x^3$ are $3x^2$ and $6x$ respectively.