Content deleted Content added
indent, periods, wording, display big expressions |
→Examples: prevent line break |
||
Line 37:
===Examples===
Several functions exist for which differentiating the inverse is much easier than differentiating the function itself. Using the inverse function theorem, a derivative of a function's inverse indicates the derivative of the original function. Perhaps the most well-known example is the method used to compute the derivative of the [[natural logarithm]], whose inverse is the [[exponential function]]. Let <math>u = \ln x</math> and restrict the ___domain to
:<math>\frac{d}{dx}\ln x = {{1} \over {\frac{d}{du}e^u}} = {{1} \over {e^u}} = {{1} \over {e^{\ln x}}} = {{1} \over {x}}.</math>
| |||