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arrow_back Determine \[ D_{x}\left(\frac{x^{3}+3 x^{2}+6 x+8}{x+2}\right) \]

by Platinum
(106,844 points)
in Mathematics
9 views
Determine
\[
D_{x}\left(\frac{x^{3}+3 x^{2}+6 x+8}{x+2}\right)
\]

1 Answer

Best answer
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Best answer
Factorise the numerator and simplify the fraction
The numerator of the fraction is a factorisable cubic polynomial, so we can factorise the numerator and simplify the fraction:
\[
\begin{aligned}
&\frac{x^{3}+3 x^{2}+6 x+8}{x+2} \\
&=\frac{(x+2)\left(x^{2}+x+4\right)}{x+2} \\
&=x^{2}+x+4
\end{aligned}
\]
Find the derivative of the resulting expression
\[
\begin{aligned}
&D_{x}\left(x^{2}+x+4\right) \\
&=2 x+1
\end{aligned}
\]
by Platinum
(106,844 points)

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