Question

question 22 - 1 point. find the derivative of (h(x)=\frac{(3x + 4)^{3}}{(-3x - 2)^{4}}). you should leave your answer in factored form. do not include \(h(x)=)\ in your answer. provide your answer below:

Explanation:

Step1: Apply quotient - rule

$h'(x)=\frac{(3x + 4)^3\cdot(-3x - 2)' - (-3x - 2)^4\cdot(3x + 4)'}{(3x + 4)^6}$

Step2: Differentiate terms

$(-3x - 2)'=-3$, $(3x + 4)' = 3$

Step3: Substitute and simplify

$h'(x)=\frac{(3x + 4)^3\cdot(-3)-(-3x - 2)^4\cdot3}{(3x + 4)^6}=\frac{-3(3x + 4)^3-3(-3x - 2)^4}{(3x + 4)^6}$

Answer:

$\frac{-3(3x + 4)^3-3(-3x - 2)^4}{(3x + 4)^6}$