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Question Number 71729 by peter frank last updated on 19/Oct/19

$$finddUifU=x^2{e}^{\frac{x}{y}}$$$$$$

Commented by peter frank last updated on 19/Oct/19

$$thankyou$$

Commented by Prithwish sen last updated on 19/Oct/19

$$\mathrm{ylnu}=2\mathrm{yln}\left(\mathrm{x}\right)+\mathrm{x}$$$$\mathbf{du}=[2{\mathbf{xe}}^{\frac{\mathbf{x}}{\mathbf{y}}}\mathbf{dx}+\frac{{\mathbf{x}}^2{\mathbf{e}}^{\frac{\mathbf{x}}{\mathbf{y}}}}{\mathbf{y}}\mathbf{dx}-\frac{{\mathbf{x}}^3}{{\mathbf{y}}^2}{\mathbf{e}}^{\frac{\mathbf{x}}{\mathbf{y}}}\mathbf{dy}]\mathbf{please}\mathbf{check}$$

Answered by mind is power last updated on 19/Oct/19

$$\mathrm{du}=\frac{\partial \mathrm{u}}{\partial \mathrm{x}}\mathrm{dx}+\frac{\partial \mathrm{u}}{\partial \mathrm{y}}\mathrm{dy}$$$$\frac{\partial }{\partial \mathrm{x}}\left({\mathrm{x}}^2{\mathrm{e}}^{\frac{\mathrm{x}}{\mathrm{y}}}\right)=(2\mathrm{x}+\frac{{\mathrm{x}}^2}{\mathrm{y}}){\mathrm{e}}^{\frac{\mathrm{x}}{\mathrm{y}}}$$$$\frac{\partial }{\partial \mathrm{y}}\left({\mathrm{x}}^2{\mathrm{e}}^{\frac{\mathrm{x}}{\mathrm{y}}}\right)=-\frac{{\mathrm{x}}^3}{{\mathrm{y}}^2}{\mathrm{e}}^{\frac{\mathrm{x}}{\mathrm{y}}}$$$$\Rightarrow \mathrm{dU}=(2\mathrm{x}+\frac{{\mathrm{x}}^2}{\mathrm{y}}){\mathrm{e}}^{\frac{\mathrm{x}}{\mathrm{y}}}\mathrm{dx}-\frac{{\mathrm{x}}^3}{{\mathrm{y}}^2}{\mathrm{e}}^{\frac{\mathrm{x}}{\mathrm{y}}}\mathrm{dy}$$

Commented by peter frank last updated on 19/Oct/19

$$thankyou$$

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