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Question Number 96467 by john santu last updated on 01/Jun/20

$$\mathrm{Suppose}\mathrm{y}=8;\frac{dy}{dx}=4\mathrm{\&}$$ $$\frac{d^{2}y}{{dx}^2}{\mid }_{x=1}=-2.\mathrm{Find}\mathrm{the}\mathrm{value}$$ $$\mathrm{of}\left(1\right)\frac{d\left(xy\right)}{dx}{\mid }_{x=1}$$ $$\left(1\right)\frac{d^2\left(xy\right)}{{dx}^2}{\mid }_{x=1}$$ $$$$

Answered by Sourav mridha last updated on 01/Jun/20

$$\left(1\right){[\mathit{x}\frac{\mathit{d}\mathit{y}}{\mathit{d}\mathit{x}}+\mathit{y}]}_{\mathit{x}=1}={[4\mathit{x}+8]}_{\mathit{x}=1}=12$$ $$\left(2\right){[\mathit{x}\frac{{\mathit{d}}^2\mathit{y}}{{\mathit{d}\mathit{x}}^2}+2\frac{\mathit{d}\mathit{y}}{\mathit{d}\mathit{x}}]}_{\mathit{x}=1}=6$$

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