List of good-to-know derivatives and integrals

Question

Can someone link me to an exhaustive list of notable derivatives/integrals?

For example, for $y= [\ln(x)]$, $\quad y^\prime = \dfrac{1}{x}$

Answer 1

See: Handbook of Mathematics (Bronshtein), for many, many of your reference needs.

You'll also want to know derivatives of trig functions; see also Wikipedia for differentiation of trig functions.

You might also want to include in your list derivatives of inverse trig functions and hyperbolic trig functions, as well. Here is a list of such functions and their derivatives and integrals: downloadable in pdf.

Of course, you'll also want to know $\frac{d}{dx}(e^x)$.

I'm assuming you've got polynomials down pat.

Here is a very nice and handy handout from "Paul's Online Math Notes": Common_Derivatives_and_Integrals.pdf.

The rest is largely a matter of knowing how to differentiate products and compositions of such functions (using chain rule, e.g.).

I wouldn't consider the list exhaustive, but it's a start!