In example 7 how did we arrive at the last step? or given

Dear Student,

Here we do not have the complete query so we assume that how we get last step from second last step ( As both steps given in provided image )

We have : $\frac{\mathrm{dy}}{\mathrm{dx}}\left(x^2 + y^2\right) = 2 x y +2 y^2\frac{\mathrm{dy}}{\mathrm{dx}}$ , So

$$\begin{gathered} \Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}\left(x^2 + y^2\right) -2 y^2\frac{\mathrm{dy}}{\mathrm{dx}}= 2 x y \\ \Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}\left(x^2 + y^2-2 y^2\right)= 2 x y \\ \Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}\left(x^2 -y^2\right)= 2 x y \\ \mathbf{\Rightarrow }\frac{\mathbf{dy}}{\mathbf{dx}}\mathbf{=}\mathbf{ }\frac{\mathbf{2}\mathbf{ }\mathbf{x}\mathbf{ }\mathbf{y}\mathbf{ }}{\left({\mathbf{x}}^{\mathbf{2}}\mathbf{ }\mathbf{-}{\mathbf{y}}^{\mathbf{2}}\right)} \end{gathered}$$

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