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Problem For x ≠ 0 x\neq0 x = 0 cos x ≠ 0 \cos x \neq0 cos x = 0 y = x 2 + 3 x + 2 x cos x y=\dfrac{x^{2}+3x+2}{x\cos x} y = x cos x x 2 + 3 x + 2 d y d x \dfrac{dy}{dx} d x d y ( x 2 − 2 ) cos x − x ( x 2 + 3 x + 2 ) sin x x 2 cos 2 x \dfrac{(x^{2}-2)\cos x - x(x^{2}+3x+2)\sin x}{x^{2}\cos^{2}x} x 2 cos 2 x ( x 2 − 2 ) cos x − x ( x 2 + 3 x + 2 ) sin x ( x 2 − 2 ) cos x + x ( x 2 + 3 x + 2 ) sin x x 2 cos 2 x \dfrac{(x^{2}-2)\cos x + x(x^{2}+3x+2)\sin x}{x^{2}\cos^{2}x} x 2 cos 2 x ( x 2 − 2 ) cos x + x ( x 2 + 3 x + 2 ) sin x ( x 2 − 2 ) cos x + ( x 2 + 3 x + 2 ) sin x x 2 cos 2 x \dfrac{(x^{2}-2)\cos x + (x^{2}+3x+2)\sin x}{x^{2}\cos^{2}x} x 2 cos 2 x ( x 2 − 2 ) cos x + ( x 2 + 3 x + 2 ) sin x ( − x 2 + 2 ) cos x − x ( x 2 + 3 x + 2 ) sin x x 2 cos 2 x \dfrac{(-x^{2}+2)\cos x - x(x^{2}+3x+2)\sin x}{x^{2}\cos^{2}x} x 2 cos 2 x ( − x 2 + 2 ) cos x − x ( x 2 + 3 x + 2 ) sin x Browse the problem library