The curve $\displaystyle y= cx + \frac{d}{x} $ has gradient 6 at the point $\displaystyle ( \frac{1}{2} , 1 ) $ find c and d

my working,

sub in the values for x and y and solve simultaneously but i dont get the right answer.....

first equation = $\displaystyle \frac{1}{2}c + \frac{d}{\frac{1}{2}} $ which I simplfied to $\displaystyle 2c + 2d = 1 $ is this simplification correct?

$\displaystyle \frac{dy}{dx} = c -dx^{-2}= 6 $

these are my two equations, and when I try to solve for 'c' and 'd' i dont get the right answer?