What is the derivative of # f(x) = (x^3-3)/x#?

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Answer 1 · 2018-03-15T05:25:56

The derivative of #f(x)# is #(2x^3+3)/(x^2)#.

#d/dx((f(x))/(g(x)))=(d/dx(f(x))*g(x)-f(x)*d/dx(g(x)))/((g(x))^2)#

Here's our expression:

#color(white)=d/dx((x^3-3)/x)#

#=(d/dx(x^3-3)*x-(x^3-3)*d/dx(x))/(x^2)#

#=((3x^2-0)*x-(x^3-3)*1)/(x^2)#

#=(3x^3-x^3+3)/(x^2)#

#=(2x^3+3)/(x^2)#

This is the derivative. Hope this helped!