Differentiate the functions w.r.t. \( x \) : \[ \frac{a x^{2}+b x+c}{p x^{2}+q x+r} \]

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Differentiate the
functions w.r.t. \( x \) :
\[
\frac{a x^{2}+b x+c}{p x^{2}+q x+r}
\]
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