derivative of x*y^3 = cos(7x+5y)
-
xy^3 = cos(7x + 5y)
x * (3y^2 * dy) + y^3 * dx = -sin(7x + 5y) * (7 * dx + 5 * dy)
3xy^2 * dy + y^3 * dx = -7 * sin(7x + 5y) * dx - 5 * sin(7x + 5y) * dy
3xy^2 * dy + 5 * sin(7x + 5y) * dy = -7 * sin(7x + 5y) * dx - y^3 * dx
dy * (3xy^2 + 5 * sin(7x + 5y)) = dx * (-7 * sin(7x + 5y) - y^3)
dy/dx = -(7 * sin(7x + 5y) + y^3) / (3xy^2 + 5 * sin(7x + 5y))
x * (3y^2 * dy) + y^3 * dx = -sin(7x + 5y) * (7 * dx + 5 * dy)
3xy^2 * dy + y^3 * dx = -7 * sin(7x + 5y) * dx - 5 * sin(7x + 5y) * dy
3xy^2 * dy + 5 * sin(7x + 5y) * dy = -7 * sin(7x + 5y) * dx - y^3 * dx
dy * (3xy^2 + 5 * sin(7x + 5y)) = dx * (-7 * sin(7x + 5y) - y^3)
dy/dx = -(7 * sin(7x + 5y) + y^3) / (3xy^2 + 5 * sin(7x + 5y))