find dy/dx if y=cosx upon 1+sinx
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y=cosx/1+sinx
dy/dx= (1+sinx).dcosx/dx-cosx.d(1+sinx)÷(1+sinx)^2
dy/dx= (1+sinx).(-sinx)-cosx.cosx÷(1+sinx)^2
dy/dx=-sinx-sin^2x-cos^2x÷(1+sinx)^2
dy/dx=-sinx-(sin^2x+cos^2x)÷(1+sinx)^2
dy/dx=-sinx-1÷(1+sinx)^2
dy/dx=-1÷1+sinx
dy/dx= (1+sinx).dcosx/dx-cosx.d(1+sinx)÷(1+sinx)^2
dy/dx= (1+sinx).(-sinx)-cosx.cosx÷(1+sinx)^2
dy/dx=-sinx-sin^2x-cos^2x÷(1+sinx)^2
dy/dx=-sinx-(sin^2x+cos^2x)÷(1+sinx)^2
dy/dx=-sinx-1÷(1+sinx)^2
dy/dx=-1÷1+sinx
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