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Friday, 5 April 2013

Functions in a bar

The Joke

All the function are gathered in a bar, drinking, chatting and relaxing. Suddenly, the x2 function enters the bar shouting with scare

- Run, run quickly, derivatives are coming and they are angry.

Then the exponential function, ex stands up, makes a step and says proudly

- Let them come, I am not afraid!




Background
When a derivative acts on function it usually changes the function's form. For example the derivative of the polynomial function decreases its order, e.g. d/dx(xn)=nxn1, where n is integer, but the result is valid for non-polynomial functions (n real) too. Other common derivatives regard the sinx and cosx functions, where d/dx(sinx)=cosx and d/dx(cosx)=sinx.

The only exception is the exponential function ex whose derivatives always give the exponential function again, i.e. d/dx(ex)=ex.




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