# List of good-to-know derivatives and integrals

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

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

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"Exhaustive" is hard when "notable" is so subjective. – Thomas Andrews Nov 26 '12 at 19:44
Notable is not that subjective. See the example. You know have a general idea of what I mean with notable. – Jijbentlekker Nov 26 '12 at 19:45
Try wikipedia here and here. – icurays1 Nov 26 '12 at 19:45
That word "subjective," I don't think it means what you think it means. Or maybe you don't know what "exhaustive" actually means. – Thomas Andrews Nov 26 '12 at 19:46
For example, the example you gave is a special case of the chain rule, $(f(g(x))'=f'(g(x))g'(x)$ where $f(y)=e^y$ and $g(x)=\ln x$, using that $(e^y)'=e^y$ and $(x)'=1$. Note, one example is not even close enough for us to determine a pattern. – Thomas Andrews Nov 26 '12 at 19:54

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!

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Thank you, exactly what I was looking for :)! – Jijbentlekker Nov 26 '12 at 20:06