Math Doubts

Derivatives of Exponential functions

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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