Using the product rule, f'(x) = d/dx(x^2 * e^x) = e^x * (x^2 + 2x).
Questions & Step-by-step Solutions
1 item
Q
Q: Determine the derivative of f(x) = x^2 * e^x.
Solution: Using the product rule, f'(x) = d/dx(x^2 * e^x) = e^x * (x^2 + 2x).
Steps: 7
Step 1: Identify the function f(x) = x^2 * e^x. This is a product of two functions: u = x^2 and v = e^x.
Step 2: Recall the product rule for derivatives. The product rule states that if you have two functions u and v, then the derivative f'(x) = u'v + uv'.
Step 3: Find the derivative of u = x^2. The derivative u' = 2x.
Step 4: Find the derivative of v = e^x. The derivative v' = e^x (since the derivative of e^x is e^x).
