Find dy/dx if x^2.y+sin(xy)+y^4.x^2+3xy=5???
x^2 y + sin(xy) + y^4 x^2 + 3xy = 5
Just use the product rule and the chain rule:
d/dx(x^2 y) = 2xy + x^2 y'
d/dx(sin(xy)) = cos(xy) (y + xy')
d/dx(x^2 y^4) = 2xy^4 + 4x^2y^3 y'
d/dx(3xy) = 3y + 3xy')
So, add them all up, collect the y' stuff, and it's all just algebra now.