Find the derivative of (x^2 - 4x)/(sqrt(x))

 (x^2 - 4x)/(sqrt(x))    We could use the quotient rule here, but we can simplify this, thusly...

x^2/x^(1/2)   -  4x / x^(1/2)  =

x^(3/2)  - 4x^(1/2)     ...and now it's easy.....

The derivative is

(3/2)x^1/2 - 2x^(-1/2)

And that's it....!!.....no messy quotient rule to worry about.....!!!