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Question Number 162847 by mkam last updated on 01/Jan/22

Answered by abdullahhhhh last updated on 01/Jan/22

$$\mathbf{you}\mathbf{want}\mathbf{vaule}\mathbf{of}\frac{\mathbf{dy}}{\mathbf{dx}}\mathbf{at}\mathbf{x}=\mathbf{\Pi }/4\mathbf{or}\mathbf{what}$$$$$$

Commented by mkam last updated on 01/Jan/22

$$yessir$$

Answered by abdullahhhhh last updated on 01/Jan/22

$$\mathbf{ln}\left(\mathbf{y}\right)=\mathbf{y}\mathbf{ln}\left(\mathbf{tanx}\right)$$$$\frac{\frac{\mathbf{dy}}{\mathbf{dx}}}{\mathbf{y}}=\mathbf{y}\frac{{\mathbf{sec}}^2\mathbf{x}}{\mathbf{tanx}}+\frac{\mathbf{dy}}{\mathbf{dx}}\mathbf{ln}\left(\mathbf{tanx}\right)$$$$\frac{\mathbf{dy}}{\mathbf{dx}}={\mathbf{y}}^2.\frac{{\mathbf{sec}}^2\mathbf{x}}{\mathbf{tanx}}+\mathbf{y}\frac{\mathbf{dy}}{\mathbf{dx}}\mathbf{ln}\left(\mathbf{tanx}\right)$$$$\frac{\mathbf{dy}}{\mathbf{dx}}\mathbf{at}\mathbf{x}=\mathbf{\Pi }/4=\frac{\mathbf{\prod }^2}{16}.\frac{2}{1}+0$$$$\frac{\mathbf{dy}}{\mathbf{dx}}=\frac{\mathbf{\prod }^2}{8}$$

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