Show that the equation of the tangent to y = 1 / x at the point for which x = p is p^2y + x = 2p. At what point on the curve is the equation of the tangent 9y + x + 6 = 0?

Differentiating:

$\displaystyle f'(x) = -1/x^2$

Then, the gradient is:

$\displaystyle f'(p) = -1 / p^2$

Shouldn't the equation be worked as follow? It's not working..

$\displaystyle y - (1 / p) = -p^-2(x - p)$