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).

**Example**

*The following calculations use *

*Next: Derivatives of Inverse Trigonometric Functions*