Question

How do you find the derivative of `y=xe^x`?

Answer 1

The derivative of y = `xe^x` is y' = `e^x + xe^x`

Explanation:

Use the product rule (u'v + v'u) to calculate the derivative:

First, write the values of u, u', v and v':

u = `x`
u' = 1
v = `e^x`
v' = `e^x`

Next, substitute these values into the product formula:

(u'v + v'u)

(1 x `e^x`) + (`e^x` x `x`) = `e^x` + `xe^x`