Can someone link me to an exhaustive list of notable derivatives/integrals?
For example, for $y= [\ln(x)]$, $\quad y^\prime = \dfrac{1}{x}$
Can someone link me to an exhaustive list of notable derivatives/integrals?
For example, for $y= [\ln(x)]$, $\quad y^\prime = \dfrac{1}{x}$
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!