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)
waec 2017furthermathematics

The correct answer is A. 10x+1

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

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

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

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

= \(10x + 1\)

Previous question Next question