Determine the derivative

Question

What is the derivative of this? How do I find it?

Answer 1

Use implicit differentiation:

sin(3x) + cos(2y) = e^4y

cos(3x)•3•dx - sin(2y)•2•dy = 4(e^4y)•dy

Divide both sides by 'dx' and re-write:

3cos(3x) - 2sin(2y)(dy/dx) = 4e^4y(dy/dx)

Solve for dy/dx:

dy/dx = 3cos(3x) / ( 2sin(2y) + 4e^4y )