y = x4 + 3x3 + 5

The function is

$$y = 2x^4 + 3x^3 + 5$$

We use the power rule for differentiation, which states that $\frac{d}{dx}(ax^n) = anx^{n-1}$, and the rule that the derivative of a constant is zero.

Differentiating the first term, $2x^4$:

$$\frac{d}{dx}(2x^4) = 2 \cdot 4x^{4-1} = 8x^3$$

Differentiating the second term, $3x^3$:

$$\frac{d}{dx}(3x^3) = 3 \cdot 3x^{3-1} = 9x^2$$

Differentiating the third term, 5:

$$\frac{d}{dx}(5) = 0$$

$$\frac{dy}{dx} = 8x^3 + 9x^2 + 0$$ $$\frac{dy}{dx} = \boxed{\mathbf{8x^3 + 9x^2}}$$