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(6x + 6y),  (0, 0)

Answer 1

(y + xy')/(1 + x²y²) = (6 + 6y')/[1 - (6x + 6y)²]^1/2; at (0, 0) we have: 0 = 6 + 6y'; y' = - 1

Equation of tangent line y = - x

Answer 2

(y + xy')/(1 + x²y²) = (6 + 6y')/[1 - (6x + 6y)²]^1/2; at (0, 0) we have: 0 = 6 + 6y'; y' = - 1

Equation of tangent line y = - x