if y=sin X + cos X /cosx, find dy /dx
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Step-by-step explanation:
y=sinx+cosx/cosx
d(u/v)/dx=vdu/dx-udv/dx/v²
d(sinx+cosx/cosx)/dx=
=(cosxd(sinx+cosx)dx-(sinx+cosx)dcosx/dx)/cos²x
=cosx(cosx-sinx)-{(sinx+cosx)× (-sinx)}/cos²x
=cos²x-sinxcosx-{ (-sin²x-sinxcosx)}/cos²x
=cos²x-sinxcosx+sin²x+sinxcosx/cos²x
=1/cos²x or sec²x
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