Question

Use this equation to find dy/dx. 9y cos(x) = x2 + y2

Answer 1

using product rule to differentiate LHS
9y×-sin(x) + cos(x) 9dy/dx
differentiate RHS
2x+2ydy/dx
equate LHS - RHS
-9ysin(x) +9cos(x)|dy/dx = 2x + 2y|dy/dx
9cos(x)dy/dx - 2ydy/dx = 2x + 9ysin(x)
(9cos(x) -2y) |dy/dx = 2x+9ysin(x)
dy/dx = (2x+9ysin(x) ) / (9cos(x) -2y)