Written by Colin+ in calculus, core 3, logarithms.
Every time you're asked to differentiate $a^x$ and you say $xa^{x-1}$, a kitten dies. A kitten that had been raised lovingly by an orphan, her only friend in the whole wide word - DEAD, just because you couldn't be bothered to learn how to do calculus properly. I hope the image of tears streaming down the poor orphan's little face haunts you forever, you cruel, heartless - yes, I'd go so far as to say vindictive - bastard.
Repeat after me: you cannot (easily) do calculus with $a^x$ as it stands. $e^x$, yes, easy. $x^n$, yes, that's easy too. But $a^x$ - any number to the power of $x$ - that's tricky.
There's a simple trick to turn it into something you can work with, though. Here are the steps:
Just... learn these things. They don't come up all that often, but when they do... well. Just learn them.
Or else the bereaved orphan kitten-owners of the world with wreak their tearful, bloody revenge on you - and we don't want that to happen now, do we?
No animals were harmed during the production of this article. Honestly.
(Image from tachyondecay used under a CC-BY licence.)