There are three differential rules for exponential functions and they are used as formulas in differential calculus to find the differentiation of exponential functions.
$\dfrac{d}{dx}{\, (x^n)} \,=\, nx^{n-1}$
The derivative of a constant base exponential function is equal to the product of the constant base exponential function and natural logarithm of the base.
$\dfrac{d}{dx}{\, (a^x)} \,=\, a^x \ln{a}$
The derivative of a natural exponential function is equal to the natural exponential function.
$\dfrac{d}{dx}{\, (e^x)} \,=\, e^x$
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