What is the derivative of #f(x)=b^x# ?

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What is the derivative of #f(x)=b^x# ?

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Answer 1 · 2014-07-23T22:15:15

This is the exponential function of base #b# (where #b>0# should be assumed). It can be thought of as #b^x=e^(xln(b))#, so that, using the Chain Rule (See Chain Rule ) and the fact that #(e^x)'=e^x# (see Exponentials with Base e ) yields #(b^x)'=e^(xln(b))\times ln(b)=b^x\times ln(b)#
(see Exponential functions ).

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What is the derivative of #f(x)=b^x# ?

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