Question

derivar (senx+ cosx/senx-cosx )

Answer 1

derivar (senx+ cosx/senx-cosx )
$\frac{dy}{dx}..\frac{senx+cosx}{senx-cosx} \\ \\ \frac{senx+cosx}{senx-cosx}= \frac{(cosx-senx)(senx-cosx)-(senx+cosx)(cosx+senx)}{(senx-cosx)^{2} } \\ .................. \frac{senxcosx-cosx^{2}-senx^{2}+senxcosx-(senxcosx+senx^{2}+cosx^{2}+senxcosx ) }{(senx-cosx)^{2} } \\ .................. \frac{2senxcosx-senx^{2}-cosx^{2}-2senxcosx-senx^{2}-cosx^{2} }{(senx-cosx)^{2} } \\ .................. \frac{-2senx ^{2}-2cosx^{2} }{(senx-cosx)^{2} } \\ ,$$\frac{-2(senx ^{2}+cosx^{2} )}{senx^{2}-2senxcosx+cosx^{2}} = \frac{-2(1)}{-2senxcosx+senx^{2}cosx ^{2} } = \frac{-2}{-2senxcosx+1}$