Derivatives of Logarithmic Functions

Proposition (Derivatives of Logarithmic Functions) The derivative of the logarithmic function is In the special case when we have and So,

        

Example (Derivatives of Logarithmic Functions) Find the equation of the tangent line to the curve at

    Solution. The derivative of is and at we have  the slope of the tangent line as Therefore, the equation of the tangent line is which simplies to
    



Example (Derivatives of Logarithmic Functions) For what values of and does satisfy

    Solution. We determine,
    




Since we find that and that can be any real number.

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