# Math Help - Implicit differentiation

1. ## Implicit differentiation

Stuck on this: A curve has the equation $x^2 - 4xy = y - 7x$. Find the gradient at the point (2,2).

2. Originally Posted by Beard
Stuck on this: A curve has the equation $x^2 - 4xy = y - 7x$. 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.

$2x - 4y - 4xy' = y' - 7$

(N.B> I used the product rule on the second term $(4xy)' = 4y + 4xy'$)

Simplifying you get

$y' = \frac{7+2x-4y}{4x+1}$

Now just substitute $x=2$, $y=2$ and you have the value of $y'$, which is the gradient.

HTH