Each card is a single, complete idea: what it is, the formulas you need, and one worked example. Built to be re-read.
For composite (nested) functions, differentiate the outside while leaving the inside alone, then multiply by the derivative of the inside. Nearly every derivative from here on needs it.
When a function sits inside a function inside a function, apply the chain rule repeatedly — work from the outermost layer inward and multiply every layer's derivative.
Use it when y is not isolated. Differentiate every term with respect to x, attaching dxdy each time you differentiate a y term, then solve algebraically for dxdy.
Differentiate repeatedly to get the second, third, or nth derivative. Done implicitly, you must substitute the first derivative back in to simplify.
An inverse swaps x and y coordinates. Its derivative is the reciprocal of the original function's derivative, evaluated at the matching point — perfect for table or single-point questions.
Memorize only arcsin, arctan, and arcsec — the co-function versions (arccos, arccot, arccsc) are identical with a negative sign. Pair them with the chain rule when the inside is more than x.