Differentiate the function y = (x3 + 3x2 + 1)5 using the chain rule.

Here are the differentiations for each function, showing all steps:

i) $y = (x^3 + 3x^2 + 1)^5$

Step 1: Apply the chain rule, $\frac{dy}{dx} = \frac{d}{du}(u^5) \cdot \frac{du}{dx}$, where $u = x^3 + 3x^2 + 1$.

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

Step 2: Differentiate $y$ with respect to $u$.

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