## importance

okay. i'm not that type of person that begs you to realize a theorem's importance. but here... things are different. this is, due to experience, the arguably most important principle in differential calculus. and it also plays a huge role in integral calculus as well.

*go make yourself a cup of coffee (better without sugar), and make sure you understand every word on this page!*## a guide to its usage

now, how do we use it? think about it as a tool to break down functions. instead of having to simplify a sometimes "unsimplifiable" function, we ignore parts of it, and try to identify a function that we are familiar with among the mess.

beginners would be dazzled with possibilities: consider the function sqrt(1-x^2). anybody with a little experience would immediately recognize the square root as the outer function, and 1-x^2 as the inner function. Now, to beginners, this is an obscure appliance because most would not recognize the pretty square root sign with the shape of a hut as a function. now, practice is the solution. practice is the key.

beginners would be dazzled with possibilities: consider the function sqrt(1-x^2). anybody with a little experience would immediately recognize the square root as the outer function, and 1-x^2 as the inner function. Now, to beginners, this is an obscure appliance because most would not recognize the pretty square root sign with the shape of a hut as a function. now, practice is the solution. practice is the key.

**for after all, you have nothing to fear-- for you have found the weakest link in the seemingly unbreakable***chain*of calculus.