For an exponential function of the form y=a^x(adsbygoogle = window.adsbygoogle || []).push({});

First derivative , d/dx [a^x ] = a^x∙ lim┬(δx→0){(a^δx-a^0)/δx}

= a^x∙ m_((0,1))

now if m_((0,1)) which is the gradient of the y-axis intersection point of the exponential function equal to 1 exactly, then the derivative will be unchanged under differentiation and the value of the base a is then considered ase(Napier constant/natural number) .

IS there any derivation to get to the napier constant??

**Physics Forums | Science Articles, Homework Help, Discussion**

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!

# Derivative of the exponential function with base e

**Physics Forums | Science Articles, Homework Help, Discussion**