exercsies 3.3 differentiation rules
score: 27/40 answered: 13/19
question 14
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if ( f(x)=\frac{3 - x^{2}}{7 + x^{2}} ), find:
( f^{prime}(x)= )
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# Explanation:
## Step1: Identify the quotient rule
The quotient rule states that if $y = \frac{u}{v}$, then $y'=\frac{u'v - uv'}{v^{2}}$. Here, $u = 3 - x^{2}$, $u'=-2x$, $v = 7 + x^{2}$, $v' = 2x$.
## Step2: Apply the quotient rule
$$
\begin{align*}
f'(x)&=\frac{(-2x)(7 + x^{2})-(3 - x^{2})(2x)}{(7 + x^{2})^{2}}\
&=\frac{-14x-2x^{3}-6x + 2x^{3}}{(7 + x^{2})^{2}}\
&=\frac{-20x}{(7 + x^{2})^{2}}
\end{align*}
$$

# Answer:
$\frac{-20x}{(7 + x^{2})^{2}}$

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Explanation:

Step1: Identify the quotient rule

Step2: Apply the quotient rule

Answer: