Home » Further Mathematics » Differentiate (frac{5x^{3} + x^{2}}{x}, xneq 0) with respect to x.

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

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

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