Derivativesof ExponentialFunctions
We havediscussedabovethat the exponentialfunctionis simplythe inversefunctionof the logarithmic
function.To obtaina derivativeformulafor the exponentialfunctionwith base we rewrite as
Differentiatingimplicitly,
Solvingfor and replacing with
Thusthe derivativeof an exponentialfunctionis
In the specialcasewherethe baseis since the derivativerule becomes
To generalize,if is a differentiablefunctionof with the use of the ChainRulethe abovederivatives
take the generalform
And if
Derivativesof ExponentialFunctions