Hi John,
x = tan(xy)
Take the derivative of each side with respect to x
d/dx [x] = d/dx [tan (xy)]
1 = [sec^2 (xy)][x dy/dx + y(1)]
The right side of the step above comes from the chain rule. Derivative of tangent is secant squared and then you have to use the product rule to find the derivative of xy.
Now, distribute the sec^2 (xy) . . .
1 = x sec^2(xy) dy/dx + y sec^2 (xy)
Now solve for dy/dx
1 - y sec^2 (xy) = x sec^2 (xy) dy/dx
[1 - y sec^2 (xy)] / x sec^2 (xy) = dy/dx
Hope this helps! :)
