A curve has an equation: (2x^2)*y +2x + 4y – cos(pi*y) = 17. Find dy/dx

You must differentiate each individual term in the equation.Firstly start with the term of the product of 2x² * y, using the product rule (dy/dx = udv/dx + vdu/dx)Let u = 2x² and v = yDu/dx = 4x and dv/dx = dy/dxDifferential of: 2x²y = 2x² dy/dx + 4xy                         2x = 2                        4y = 4 dy/dx                        -cos(piy) = pi * dy/dx sin(piy)                        17 = 0So overall differential of whole equation:              2x² dy/dx + 4xy + 2 + 4 dy/dx + pidy/dx sin(piy) = 0Rearrange the equation to get any term that contains a dy/dx on one side:              2x² dy/dx + 4 dy/dx + pidy/dx sin(piy) = - 4xy – 2Take out a factor of dy/dx on the left hand side:Dy/dx(2x² + 4 + pisin(piy)) = - 4xy -2Divide by the other term on the left hand side to get dy/dx by itself:Dy/dx = (-4xy – 2)/( 2x² + 4 + pisin(piy))