In details

Derivatives of Exponential Functions

To get a formula for the derivative of exponential functions

y =

we rewrite this equation as

x =

and differentiate implicitly using to get

that we can rewrite using y = as

Thus, showing that if is a differentiable function, so its derivative with respect to x é

In the special case where b = e we have 1n and = 1n, like this becomes

In addition, if u is a differentiable function of xthen one has from and what

NOTE.It is important to distinguish between (variable exponent and constant basis) and (variable base and constant exponent).


The following calculations use

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