Differentiate y=(x+2)(x+5)

1. Apply the product rule: \frac{d}{dx} [u \cdot v] = u' \cdot v + u \cdot v'

2. Let \( u = x + 2 \) and \( v = x + 5 \).

3. Differentiate \( u \): u' = 1

4. Differentiate \( v \): v' = 1

5. Apply the product rule:
y' = (x + 2) \cdot 1 + (x + 5) \cdot 1

6. Simplify:
y' = (x + 2) + (x + 5)
y' = 2x + 7

Answer:
y' = 2x + 7