Determine dy/dx for each of the following. Write answers in terms of x and y.

1. 3x²-6y⁵+3=ln x
2. 2x² y⁸-6y⁵+3x²=5
3. sec(xy)+sin(y)=tan(x)
4. ln(y)-3cos(x+y)+x/y=6
5. 12sqrt(x²-y²) - 3e^4y-5x⁷+14xcosy=e(pi)