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Class-11-science»Maths

If y=x³+5x/x*logx+3cotx find dy/dx

y = \frac{x^{3} + 5 x}{xlogx + 3 cotx} So \frac{dy}{dx} = \frac{d}{dx} (\frac{x^{3} + 5 x}{xlogx + 3 cotx}) = \frac{(xlogx + 3 cotx) \frac{d}{dx} (x^{3} + 5 x) - (x^{3} + 5 x) \frac{d}{dx} (xlogx + 3 cotx)}{{(xlogx + 3 cotx)}^{2}} = \frac{(xlogx + 3 cotx) (3 x^{2} + 5) - (x^{3} + 5 x) (1 + logx - 3 {cosec}^{2} x)}{{(xlogx + 3 cotx)}^{2}}

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