The curve C has equation 2yx^2 + 2x + 4y - cos(πy) = 45. Using implicit differentiation, find dy/dx in terms of x and y
2x2y + 2x + 4y - cos(πy) = 45Applying implicit differentiation:4xy + 2x2(dy/dx) + 2 + 4(dy/dx) + πsin(πy)(dy/dx) = 0Moving all (dy/dx) terms to one side:2x2 (dy/dx) + 4(dy/dx) + πsin(πy)(dy/dx) = -4xy - 2Factorising:dy/dx [ 2x2 + 4 +πsin(πy) ] = -(4xy + 2)Making (dy/dx) the subject of the equation:dy/dx = -(4xy + 2) / 2x2 + 4 +πsin(πy)
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