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There are three differential rules for exponential functions and they are used as formulas in differential calculus to find the differentiation of exponential functions.

Power Rule

$\dfrac{d}{dx}{\, (x^n)} \,=\, nx^{n-1}$

Constant Base Power Rule

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.

$\dfrac{d}{dx}{\, (a^x)} \,=\, a^x \ln{a}$

Natural Power Rule

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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