Take note of .
Now the problem reduces to finding if then
lim 3^(4+h) - 3^(4)
i think i remember something from calc that had to do with the definition of a derivative, and a variation of the formula looking something similiar to this... any help?? i dont know where to begin...
the rule is genrally derived by using the chain rule (once we know the derivative of ) and not by evaluating the limit directly.
we use the fact that and
so, by the chain rule. which simplifies to for
so recognizing that it is the derivative limit and running the above proof is the way to go
an alternative to find the limit without this, is to use a slightly modified version of the difference quotient, and some knowledge of hyperbolic functions.
let . this is equivalent to the previous definition. we just used the points and as opposed to and .