How do you differentiate (x^2-5x+2)/root3x?

1 Answer
Oct 14, 2015

dy/dx = (5x^(2/3) + 10x^(-5/6) + 2x^(-4/3))/3

Explanation:

The simplest way is to put the function into exponential notation, foil them and then derivate

y = (x^2 - 5x + 2)/root(3)(x)

y = (x^2 - 5x + 2)*(x^(-1/3))

y = x^(2-1/3) - 5x^(1-1/3) + 2x^(-1/3)

y = x^(5/3) - 5x^(-2/3) + 2x^(-1/3)

dy/dx = (5x^(2/3))/3 -(5*(-2)*x^(-5/6))/3 + (2x^(-4/3))/3

dy/dx = (5x^(2/3) + 10x^(-5/6) + 2x^(-4/3))/3