Stuck on this: A curve has the equation $\displaystyle x^2 - 4xy = y - 7x$. Find the gradient at the point (2,2).
You can differentiate both sides with respect to x remembering that y is a function of x.
$\displaystyle 2x - 4y - 4xy' = y' - 7$
(N.B> I used the product rule on the second term $\displaystyle (4xy)' = 4y + 4xy'$)
Simplifying you get
$\displaystyle y' = \frac{7+2x-4y}{4x+1}$
Now just substitute $\displaystyle x=2$, $\displaystyle y=2$ and you have the value of $\displaystyle y'$, which is the gradient.
HTH