y=log(senx) Proove the d3y/dx2=2cos...
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( y=log (operatorname{sen} x) quad ) Proove the (frac{d^{3} y}{d x^{2}}=2 cos x cdot operatorname{cosec}^{3} x )

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y=log(senx) Proove the d3y/dx2=2cosx⋅cosec^3x
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( begin{aligned} y &=log (sin x) frac{d y}{d x} &=frac{(cos x)}{sin x}=cot x frac{d^{2} y}{d x^{2}}=-operatorname{cosec}^{2} x Rightarrow frac{d^{3} y}{d x^{2}} &=-2 operatorname{cosec} x-(operatorname{cosec} x cot x) text { prois } &=2 operatorname{cosec}^{2} x frac{cos x}{sin x} &=2 operatorname{cosec}^{3} x cos x end{aligned} )

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