Question Number 162847 by mkam last updated on 01/Jan/22
Answered by abdullahhhhh last updated on 01/Jan/22
$$\boldsymbol{\mathrm{you}}\:\boldsymbol{\mathrm{want}}\:\boldsymbol{\mathrm{vaule}}\:\boldsymbol{\mathrm{of}}\frac{\boldsymbol{\mathrm{dy}}}{\boldsymbol{\mathrm{dx}}}\:\boldsymbol{\mathrm{at}}\:\boldsymbol{\mathrm{x}}=\boldsymbol{\Pi}/\mathrm{4}\:\boldsymbol{\mathrm{or}}\:\boldsymbol{\mathrm{what}} \\ $$$$ \\ $$
Commented by mkam last updated on 01/Jan/22
$${yes}\:{sir} \\ $$
Answered by abdullahhhhh last updated on 01/Jan/22
$$\boldsymbol{\mathrm{ln}}\left(\boldsymbol{\mathrm{y}}\right)=\boldsymbol{\mathrm{y}}\:\boldsymbol{\mathrm{ln}}\left(\boldsymbol{\mathrm{tanx}}\right) \\ $$$$\frac{\frac{\boldsymbol{\mathrm{dy}}}{\boldsymbol{\mathrm{dx}}}}{\boldsymbol{\mathrm{y}}}=\boldsymbol{\mathrm{y}}\:\frac{\boldsymbol{\mathrm{sec}}^{\mathrm{2}} \boldsymbol{\mathrm{x}}}{\boldsymbol{\mathrm{tanx}}}+\frac{\boldsymbol{\mathrm{dy}}}{\boldsymbol{\mathrm{dx}}}\:\boldsymbol{\mathrm{ln}}\left(\boldsymbol{\mathrm{tanx}}\right) \\ $$$$\frac{\boldsymbol{\mathrm{dy}}}{\boldsymbol{\mathrm{dx}}}=\boldsymbol{\mathrm{y}}^{\mathrm{2}} .\frac{\boldsymbol{\mathrm{sec}}^{\mathrm{2}} \boldsymbol{\mathrm{x}}}{\boldsymbol{\mathrm{tanx}}}+\boldsymbol{\mathrm{y}}\:\frac{\boldsymbol{\mathrm{dy}}}{\boldsymbol{\mathrm{dx}}}\:\boldsymbol{\mathrm{ln}}\left(\boldsymbol{\mathrm{tanx}}\right) \\ $$$$\frac{\boldsymbol{\mathrm{dy}}}{\boldsymbol{\mathrm{dx}}}\:\boldsymbol{\mathrm{at}}\:\boldsymbol{\mathrm{x}}=\boldsymbol{\Pi}/\mathrm{4}=\:\frac{\boldsymbol{\prod}^{\mathrm{2}} }{\mathrm{16}}.\frac{\mathrm{2}}{\mathrm{1}}+\mathrm{0} \\ $$$$\frac{\boldsymbol{\mathrm{dy}}}{\boldsymbol{\mathrm{dx}}}=\frac{\boldsymbol{\prod}^{\mathrm{2}} }{\mathrm{8}} \\ $$