Hey, I am having some difficulties. So it's my understanding that the function e(adsbygoogle = window.adsbygoogle || []).push({}); ^{x}comes around out of a desire to have a function whose derivative is equal to itself. Well we can show that if f(x)=a^{x}, a>0, then f'(x) is equal to a multiple of itself using the limit definition of the derivative

f'(x) = lim h-->0 (f(x+h)-f(x))/h = lim h-->0 (a^{x+h}- a^{x})/h = lim h-->0 a^{x}(a^{h}-1)/h = a^{x}( lim h-->0 (a^{h}-1)/h )

So the goal is, if we can find a value a that makes (lim h--> 0 (a^{h}-1)/h ) = 1, then f'(x) = f(x).

My only issue is that when I actually take this limit, I don't understand how it can be anything other than 0.

lim h-->0 (a^{h}-1)/h ) = 0/0 so if we apply L'hopitals, we get

lim h-->0 (h*a^{h-1})/(1) = [lim h--> 0 (h) * lim h-->0 (a^{h-1})]/lim h-->0 (1) = 0

Right? What am I doing wrong in evaluating this limit? I mean I know I"m doing something wrong I just can't figure out what it is

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Deriving the value of e

Loading...

Similar Threads for Deriving value | Date |
---|---|

I Multivariable Analysis ...the derivative & the differential | Feb 27, 2018 |

I Derivative of a Real-Valued Function of Several Variables... | Feb 25, 2018 |

I Derivative of a Vector-Valued Function of a Real Variable .. | Feb 24, 2018 |

I Directional Derivatives ... Notation ... D&K ... | Feb 22, 2018 |

Inequality integral absolute value derivative | Nov 17, 2013 |

**Physics Forums - The Fusion of Science and Community**