4. -/1 points details my notes differentiate. g(x) = (5x - 1)/(2x + 1) g(x) = need help? read it watch it…

Explanation:

Step1: Apply quotient - rule

The quotient - rule states that if $g(x)=\frac{u(x)}{v(x)}$, then $g^{\prime}(x)=\frac{u^{\prime}(x)v(x)-u(x)v^{\prime}(x)}{v(x)^2}$. Here, $u(x)=5x - 1$, $u^{\prime}(x)=5$, $v(x)=2x + 1$, and $v^{\prime}(x)=2$.

Step2: Substitute into quotient - rule formula

$g^{\prime}(x)=\frac{5(2x + 1)-(5x - 1)\times2}{(2x + 1)^2}$.

Step3: Expand numerator

$g^{\prime}(x)=\frac{10x+5-(10x - 2)}{(2x + 1)^2}=\frac{10x + 5-10x + 2}{(2x + 1)^2}$.

Step4: Simplify numerator

$g^{\prime}(x)=\frac{7}{(2x + 1)^2}$.

Answer:

$\frac{7}{(2x + 1)^2}$