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

Explanation

This can be done either by using quotient rule or by direct division of the equation, then differentiate.

\(\frac{\mathrm d}{\mathrm d x} \left( \frac{5x^{3} + x^{2}}{x} \right)\)

= \(\frac{\mathrm d}{\mathrm d x} \left ( \frac{5x^{3}}{x} + \frac{x^{2}}{x} \right)\)

= \(\frac{\mathrm d}{\mathrm d x} \left ( 5x^{2} + x \right)\)

= \(10x + 1\)