<p>A couple of things that may or may not help:</p>
<p>If you’re taking the derivative of a non-cofunction (sin, tan, or sec), than the deriviative of the corresponding cofunction (cos, cot, or csc) switches “co”-status and also has a negative. This relationship is probably best described in the pattern below.</p>
<p>So, d/dx[sin x] = cos x and d/dx[cos x] = -sin x
d/dx [tan x] = sec^2 x and d/dx[cot x] = -csc^2 x
d/dx [sec x] = sec x tan x and d/dx [csc x] = -csc x cot x</p>
<p>Which means if you can remember the relationship between the derivative of a trig function and the derivative of its cofunction, you only need to memorize the first entry in each row.</p>
<p>Though honestly, if you think memorizing trig derivatives is hard, wait until inverse trig functions come around. :)</p>