# How to Differentiate the Trigonometric Functions

You should memorize the derivatives of the six trig functions. Make sure you memorize the first two in the following list — they’re a snap. If you’re good at rote memorization, memorize the last four as well.

Here they are:

You might enjoy the following mnemonic trick for the last four trig derivatives. (This might seem a bit convoluted, but it works). Imagine you’re taking a test and can’t remember these derivatives. You lean over to the guy next to you and whisper, “Psst, hey, what’s the derivative of csc*x?*” Now, take the last three letters of *psst* (sst) — those are the initial letters of sec*, *sec*, *tan*.* Write these three functions down, and below them, write their cofunctions:* *csc*, *csc*, *cot*. *Put a negative sign on the csc in the middle. Finally, add arrows:

Using this diagram, the trig derivatives are very easy to remember. Look at the top row. The *sec* on the left has an arrow pointing to *sec tan* — so the derivative of sec*x* is sec*x** *tan*x.*

The bottom row works the same way, except that both derivatives are negative.