Question: What is the derivative of f(x) = x^2 * e^x?
Options:
e^x(2x + x^2)
e^x(2x)
e^x(x^2 + 2)
e^x(x^2 + 1)
Correct Answer: e^x(2x + x^2)
Solution:
Using the product rule, f\'(x) = e^x * (x^2 + 2x).
What is the derivative of f(x) = x^2 * e^x?
Practice Questions
Q1
What is the derivative of f(x) = x^2 * e^x?
e^x(2x + x^2)
e^x(2x)
e^x(x^2 + 2)
e^x(x^2 + 1)
Questions & Step-by-Step Solutions
What is the derivative of f(x) = x^2 * e^x?
Correct Answer: f'(x) = e^x * (x^2 + 2x)
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).
