I want to double check these answers, this book doesnt supply answers.

1

$\displaystyle y= \frac{5x^4-3x}{x^2}\ $

$\displaystyle y= 4x^2-2x^-1 $

$\displaystyle \frac{dy}{dx}\ = 8x+2x^-2 $

$\displaystyle 8x+\frac{2}{x^2}\ $

2

$\displaystyle f(x)=(\frac{1}{x^2}+2)(x-3) $

$\displaystyle f(x)=(x^-2+2)(x-3) $

$\displaystyle f(x)= x^-1-3x^2+2x-6 $

$\displaystyle f'(x)= x^-1-6x^-3+2 $

$\displaystyle = \frac{-1}{x^2}\ + \frac{6}{x^3}+2 $

3

$\displaystyle y= \frac{2\sqrt(x)}{x} $

$\displaystyle y= 2x^\frac{-1}{2} $

$\displaystyle \frac{dy}{dx} = -x^\frac{-3}{2} $

$\displaystyle = -\frac{1}{x^\frac{3}{2}} $

Thanx in advance :D