Step 1: Identify the function f(x) = 4x^2 * e^x. This is a product of two functions: u = 4x^2 and v = e^x.
Step 2: Recall the product rule for differentiation. The product rule states that if you have two functions u and v, then the derivative f'(x) = u'v + uv'.
Step 3: Differentiate u = 4x^2. The derivative u' = 8x.
Step 4: Differentiate v = e^x. The derivative v' = e^x (since the derivative of e^x is e^x).
