Differentiate \(\frac{5x^{3} + x^{2}}{x}, x\neq 0\) with respect to x.
A. 10x+1
B. 10x+2
C. x(15x+1)
D. x(15x+2)
Correct Answer: A
Explanation
This can be done either by using quotient rule or by direct division of the equation, then differentiate.
\(\frac{\mathrm d}{\mathrm d x} \left( \frac{5x^{3} + x^{2}}{x} \right)\)
= \(\frac{\mathrm d}{\mathrm d x} \left ( \frac{5x^{3}}{x} + \frac{x^{2}}{x} \right)\)
= \(\frac{\mathrm d}{\mathrm d x} \left ( 5x^{2} + x \right)\)
= \(10x + 1\)
