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)