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

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Answer 1 · 2015-10-14T01:53:18

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

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#