mcq practice (no calculator) 1 multiple choice 1 point if f(x)=3x - 2 / 2x + 3, then f(x)=(a) - 13 / (2x +…

mcq practice (no calculator) 1 multiple choice 1 point if f(x)=3x - 2 / 2x + 3, then f(x)=(a) - 13 / (2x + 3)^2 (b) 3 / (2x + 3)^2 (c) 5 / (2x + 3)^2 (d) 13 / (2x + 3)^2 (e) 12x + 5 / (2x + 3)^2

mcq practice (no calculator) 1 multiple choice 1 point if f(x)=3x - 2 / 2x + 3, then f(x)=(a) - 13 / (2x + 3)^2 (b) 3 / (2x + 3)^2 (c) 5 / (2x + 3)^2 (d) 13 / (2x + 3)^2 (e) 12x + 5 / (2x + 3)^2

Answer

Explanation:

Step1: Apply quotient - rule

The quotient - rule states that if $f(x)=\frac{u(x)}{v(x)}$, then $f^{\prime}(x)=\frac{u^{\prime}(x)v(x)-u(x)v^{\prime}(x)}{v(x)^2}$. Here, $u(x)=3x - 2$, $u^{\prime}(x)=3$, $v(x)=2x + 3$, and $v^{\prime}(x)=2$.

Step2: Substitute into quotient - rule formula

$f^{\prime}(x)=\frac{3(2x + 3)-(3x - 2)\times2}{(2x + 3)^2}$.

Step3: Expand the numerator

Expand $3(2x + 3)-(3x - 2)\times2$: $3(2x+3)=6x + 9$ and $(3x - 2)\times2 = 6x-4$. So, $6x + 9-(6x - 4)=6x + 9-6x + 4$.

Step4: Simplify the numerator

$6x+9 - 6x + 4=13$. So, $f^{\prime}(x)=\frac{13}{(2x + 3)^2}$.

Answer:

D. $\frac{13}{(2x + 3)^2}$