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Earlier discussion
1 older comment kept for context.
Victor Titus
This can be done either by using quotient rule or by direct division of the equation, then differentiate.
\(\frac{\mathrm d}{\mathrm d x} \left( \frac{5x^{3} + x^{2}}{x} \right)\)
= \(\frac{\mathrm d}{\mathrm d x} \left ( \frac{5x^{3}}{x} + \frac{x^{2}}{x} \right)\)
= \(\frac{\mathrm d}{\mathrm d x} \left ( 5x^{2} + x \right)\)
= \(10x + 1\)