Question

section 3.3 derivatives and quotients
question 4, 3.3.12
find f(x).
f(x) = (3x + 9)(6x - 5)
f(x) =
(type an exact answer.)

Explanation:

Step1: Apply product - rule

The product - rule states that if $y = u(x)v(x)$, then $y^\prime=u^\prime(x)v(x)+u(x)v^\prime(x)$. Let $u(x)=3x + 9$ and $v(x)=6x - 5$.

Step2: Find $u^\prime(x)$ and $v^\prime(x)$

Differentiate $u(x)$: $u^\prime(x)=\frac{d}{dx}(3x + 9)=3$. Differentiate $v(x)$: $v^\prime(x)=\frac{d}{dx}(6x - 5)=6$.

Step3: Substitute into product - rule

$f^\prime(x)=u^\prime(x)v(x)+u(x)v^\prime(x)=3(6x - 5)+(3x + 9)\times6$.

Step4: Expand and simplify

$$
LATEXBLOCK0
$$

Answer:

$36x + 39$