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We need to differentiate each term of x2 sin y - e2y cos x = 3x2 + 2x - 5 with respect to x implicitly.1. d/dx (x2 sin y): Using the product rule: (d/dx [x2]) sin y + x2 (d/dx [sin y]) = 2x sin y + x2 (cos y * dy/dx)2. d/dx (e2y cos x): Using the product rule: (d/dx [e2y]) cos x + e2y (d/dx [cos x]) = (e2y * 2 * dy/dx) cos x + e2y (-sin x) = 2e2y cos x (dy/dx) - e2y sin x3. d/dx (3x2 + 2x - 5): = 6x + 2 - 0 = 6x + 2Substitute these back into the differentiated equation:(2x sin y + x2 cos y (dy/dx)) - (2e2y cos x (dy/dx) - e2y sin x) = 6x + 22x sin y + x2 cos y (dy/dx) - 2e2y cos x (dy/dx) + e2y sin x = 6x + 2Group terms with dy/dx:dy/dx (x2 cos y - 2e2y cos x) = 6x + 2 - 2x sin y - e2y sin xSolve for dy/dx:dy/dx = (6x + 2 - 2x sin y - e2y sin x) / (x2 cos y - 2e2y cos x)This matches option C.