Use implicit differentiation to find an equation of the tangent line to the graph of the equation at the given point.

Question

arctan(xy) = arcsin(5x + 5y),  (0, 0)

Answer 1

If you have a graphing calculator, graph this function near the origin to see what is going on.

Then do the implicit differentiation which looks like a mess, but comes out simply at the origin.

(I won't try to show you the mess, try it yourself!)

The derivative turns out to be -1 and the tangent line is therefore y=-x