Friday, June 3, 2011

exponential functions in calculus

Exponential function (and its twin sister the logarithmic) is one of the top 3 most important functions in finance. (Can't name the others though.)

Derivative of the standard exponential function exp(x) is exp(x) itself. Consequently, 2nd derivative (and nth derivative) is again itself. Furthermore, when you know that a mysterious function's derivative function is itself, you may wonder whether that function is related to exp(). Answer is that function must be exp(). No one else have this unique property.

All exponential functions (i.e. functions whose x is the exponent, i.e. up there) are related to the standard exponential function exp(x)=ex. This makes the standard exponential function very useful esp. in calculus.

5x is also commonly written as 5^x or 5**x
3(2x)
(5x)y 
5(x)^3.1

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