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??

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# Derivative of the exponential function with base e

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