Question

Differentiate. y = (x2 - 2x + 6) et O (2x - 2) ex (x2 + 4x + 4) ex O (x2 + 4) ex + 4x + 6​

Answer 1

y' = (x² + 4)eˣ

Explanation:

Power rule: y' = f'(x)g(x) + f(x)g'(x)

`(d)/(dx) [e^x]=e^x`

Step 1: Write equation

y = (x² - 2x + 6)eˣ

Step 2: Differentiate

1. Power rule: y' = eˣ(2x - 2) + eˣ(x² - 2x + 6)
2. Factor out eˣ: y' = eˣ[2x - 2 + x² - 2x + 6]
3. Combine like terms: y' = eˣ(x² + 4)
4. Rewrite: y' = (x² + 4)eˣ