differentiate x2 +sinx divided by xcosx

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Solution

$\frac{d}{d x} (\frac{x^{2} + \sin x}{x \cos x}) A s \frac{d}{d x} (\frac{u}{v}) = \frac{u' v - v' u}{v^{2}} H e n c e \frac{d}{d x} (\frac{x^{2} + \sin x}{x \cos x}) = \frac{(2 x + \cos x) x \cos x - (\cos x - x \sin x) (x^{2} + \sin x)}{(x \cos x)^{2}} = \frac{2 x^{2} \cos x + x \cos^{2} x - (x^{2} \cos x - x^{3} \sin x + \sin x \cos x - x \sin^{2} x)}{(x \cos x)^{2}} = \frac{x^{2} \cos x + x - \sin x \cos x + x^{3} \sin x}{(x \cos x)^{2}}$

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