The problem is to find the second derivative of the function $y = 20x^3$. We need to find $y''$.

1. Problem Description

The problem is to find the second derivative of the function $y = 20x^3$. We need to find $y''$.

2. Solution Steps

First, we find the first derivative, $y'$, with respect to $x$.

The power rule for differentiation states that if $y = ax^n$, then $\frac{dy}{dx} = nax^{n-1}$.

Applying the power rule:

$y = 20x^3$

$y' = \frac{d}{dx}(20x^3) = 3 \cdot 20x^{3-1} = 60x^2$

Now, we find the second derivative, $y''$, which is the derivative of $y'$ with respect to $x$.

$y' = 60x^2$

$y'' = \frac{d}{dx}(60x^2) = 2 \cdot 60x^{2-1} = 120x$

3. Final Answer

The second derivative is $y'' = 120x$.