Using the product rule: f'(x) = x^2 * e^x + 2x * e^x = e^x(x^2 + 2x).
Questions & Step-by-step Solutions
1 item
Q
Q: Find the derivative of f(x) = x^2 * e^x.
Solution: Using the product rule: f'(x) = x^2 * e^x + 2x * e^x = e^x(x^2 + 2x).
Steps: 9
Step 1: Identify the function f(x) = x^2 * e^x. This is a product of two functions: x^2 and e^x.
Step 2: Recall the product rule for derivatives. The product rule states that if you have two functions u(x) and v(x), then the derivative of their product is u'v + uv'.
Step 3: Assign u = x^2 and v = e^x. Now we need to find the derivatives of u and v.
Step 4: Calculate the derivative of u: u' = d/dx(x^2) = 2x.
Step 5: Calculate the derivative of v: v' = d/dx(e^x) = e^x.
