Question

question. for $j(x)=\frac{x^{2}}{3x + 7}$, find $j(x)$ by applying the quotient rule. provide your answer below:

Explanation:

Step1: Recall quotient - rule

The quotient - rule states that if $y=\frac{u}{v}$, then $y'=\frac{u'v - uv'}{v^{2}}$. Here, $u = x^{2}$ and $v=3x + 7$.

Step2: Find $u'$ and $v'$

$u'=\frac{d}{dx}(x^{2}) = 2x$, $v'=\frac{d}{dx}(3x + 7)=3$.

Step3: Apply quotient - rule

$j'(x)=\frac{2x(3x + 7)-x^{2}\times3}{(3x + 7)^{2}}=\frac{6x^{2}+14x - 3x^{2}}{(3x + 7)^{2}}=\frac{3x^{2}+14x}{(3x + 7)^{2}}$.

Answer:

$\frac{3x^{2}+14x}{(3x + 7)^{2}}$