$a^x$ = Any number raised to the x

Base Case: $a^{\mathrm{(}x\mathrm{)}}$

Note :

–          This is the case where a is any number raised to the x .

–          It is the more general case of the $e^{\mathrm{(}x\mathrm{)}}$special case.

–          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.