Differentiating exponential and logarithmic functions involves special rules. No worries — once you memorize a couple of rules, differentiating these functions is a piece of cake.

**Exponential functions:**If you can’t memorize this rule, hang up your calculator.Look at the graph of

*y*=*e*in the following figure.^{x}Pick any point on this function, say (2, ~7.4). The height of the function at that point, ~7.4, is the same as the slope at that point.

If the base of the logarithmic function is a number other than

*e*, you have to tweak the derivative by multiplying it by the natural log of the base. Thus,**Logarithmic functions:**And now — can you guess? — the derivatives of logarithmic functions. Here’s the derivative of the*natural*log — that’s the log with base*e:*If the log base is a number other than

*e,*you tweak this derivative — like with exponential functions — except that you*divide*by the natural log of the base instead of multiplying. Thus,