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Derivatives of Exponential and Logarithmic Functions ...

Calculus 2. Lia Vas Derivatives of Exponential and Logarithmic Functions . Logarithmic Differentiation Derivative of Exponential Functions . The natural Exponential function can be considered as the easiest function in Calculus courses since the derivative of ex is ex . General Exponential Function ax . Assuming the formula for ex , you can obtain the formula x for the derivative of any other base a > 0 by noting that y = ax is equal to eln a = ex ln a . Use chain rule and the formula for derivative of ex to obtain that y 0 = ex ln a ln a = ax ln a. Thus the derivative of ax is ax ln a. Derivative of the inverse function. If f (x) is a one-to-one function ( the graph of f (x). passes the horizontal line test), then f (x) has the inverse function f 1 (x).

Derivatives of Exponential and Logarithmic Functions. Logarithmic Di erentiation Derivative of exponential functions. The natural exponential function can be considered as \the easiest function in Calculus courses" since the derivative of ex is ex: General Exponential Function a x. Assuming the formula for e ; you can obtain the formula

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