$e^x$

Base Case: $e^x$

Note :

–          Remember e is a number, like π. Like π it showed up all the time in math so it got its own name, its own button on the calculator, it is NOT a variable.

–          Keep in mind that as soon as whatever is inside the function, inside the parenthesis, is more than just your basic x , the problem’s primary rule becomes a chain rule. Whatever you replace the x with inside your base special case will become the inside piece of your chain rule.

–          Also, when you apply the chain rule, everywhere you see an x in the $f\prime \left(x\right)$ equations above, you will plug in the full inside piece.

–          You will need to know this table equally as well in both directions, left to right and right to left.