Calculus problem

Question

Is the following true or false?

Options:

1. True
2. False

Answer 1

x²*e^x is a product so we must use the product rule to find the derivative. The Product Rule is:

[f(x) * g(x)] ' = f '(x)*g(x) + f(x)*g'(x)

Let f(x) = x² meaning f '(x) = 2x

Let g(x) = e^x meaning g'(x) = e^x

[f(x) * g(x)] ' = 2x*e^x + x² *e^x

There are common factors of "e^x " and "x" so we can factor those out to get:

xe^x(2 + x) or xe^x(x + 2) so this is true