Fnc to the 2nd pematical L = 4x3 − 5x + 3x2

We differentiate each term of the function with respect to $x$:

$$\frac{dZ}{dx} = \frac{d}{dx}(4x^3) - \frac{d}{dx}(5x^2) + \frac{d}{dx}(3x)$$

Applying the power rule:

$$\frac{dZ}{dx} = (3 \cdot 4x^{3-1}) - (2 \cdot 5x^{2-1}) + (1 \cdot 3x^{1-1})$$ $$\frac{dZ}{dx} = 12x^2 - 10x^1 + 3x^0$$ $$\frac{dZ}{dx} = 12x^2 - 10x + 3$$

We differentiate the first derivative, $\frac{dZ}{dx}$, with respect to $x$:

$$\frac{d^2Z}{dx^2} = \frac{d}{dx}(12x^2 - 10x + 3)$$

Differentiating each term:

$$\frac{d^2Z}{dx^2} = \frac{d}{dx}(12x^2) - \frac{d}{dx}(10x) + \frac{d}{dx}(3)$$

Applying the power rule:

$$\frac{d^2Z}{dx^2} = (2 \cdot 12x^{2-1}) - (1 \cdot 10x^{1-1}) + 0$$ $$\frac{d^2Z}{dx^2} = 24x^1 - 10x^0$$ $$\frac{d^2Z}{dx^2} = 24x - 10$$

The first derivative is:

$$\boxed{\frac{dZ}{dx} = 12x^2 - 10x + 3}$$

The second derivative is:

$$\boxed{\frac{d^2Z}{dx^2} = 24x - 10}$$