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))
