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Differentiate $\frac{5 x^{3}+x^{2}}{x}, x \neq 0$ with respect to $x$

A. $10 x+1$
B. $10 x+2$
C. $x(15 x+1)$
D. $x(15 x+2)$
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Correct Answer:

Option $A$

Explanation
This can be done either by using quotient rule or by direct division of the equation, then differentiate.
\begin{aligned} &\frac{\mathrm{d}}{\mathrm{d} x}\left(\frac{5 x^{3}+x^{2}}{x}\right) \\ &=\frac{\mathrm{d}}{\mathrm{d} x}\left(\frac{5 x^{3}}{x}+\frac{x^{2}}{x}\right) \\ &=\frac{\mathrm{d}}{\mathrm{d} x}\left(5 x^{2}+x\right) \\ &=10 x+1 \end{aligned}

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