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The derivative of tan(X) Since tan(X)=sin(X)/cos(X), we have sin(X) as the function u(X) and cos(X) as the function v(X). Putting these into the formula d[uv]/dX=(vdu/dX - udv/dX)/v2 we get d[tan(X)]/dX = (cos(X)cos(X) + sin(X)sin(X))/cos2(X) But on the top we have sin2(X)+ cos2(X), which is always 1. So our result simplifies to d[tan(X)]/dX = 1/cos2(X). But that is sec2(X), since sec(X)=1/cos(X).
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