Find the derivative of y = 3x6 and y = 2x3 − 3x2 + 12x.

To differentiate $y = 3x^6$, use the power rule for differentiation, which states that if $y = ax^n$, then $\frac{dy}{dx} = n \cdot ax^{n-1}$.
Here, $a = 3$ and $n = 6$.

$$\frac{dy}{dx} = 6 \cdot 3x^{6-1}$$ $$\frac{dy}{dx} = 18x^5$$

To differentiate $y = 2x^3 - 3x^2 + 12x$, differentiate each term separately using the power rule.

Differentiate the first term, $2x^3$:

$$\frac{d}{dx}(2x^3) = 3 \cdot 2x^{3-1} = 6x^2$$

Differentiate the second term, $-3x^2$:

$$\frac{d}{dx}(-3x^2) = 2 \cdot (-3)x^{2-1} = -6x$$

Differentiate the third term, $12x$:

$$\frac{d}{dx}(12x) = 1 \cdot 12x^{1-1} = 12x^0 = 12 \cdot 1 = 12$$

Combine the derivatives of each term:

$$\frac{dy}{dx} = 6x^2 - 6x + 12$$

a) The derivative of $y = 3x^6$ is $\boxed{18x^5}$.

b) The derivative $\frac{dy}{dx}$ of $y = 2x^3 - 3x^2 + 12x$ is $\boxed{6x^2 - 6x + 12}$.