What is the derivative of #pi^x#?

1 Answer
sente
Jun 26, 2016

#d/dxpi^x = pi^xln(pi)#

Explanation:

#d/dxpi^x = d/dx e^ln(pi^x)#

#=d/dxe^(xln(pi))#

#=e^(xln(pi))(d/dxxln(pi))#

(By applying the chain rule with the functions #e^x# and #xln(pi)#)

#=e^ln(pi^x)ln(pi)#

#=pi^xln(pi)#

Note that this method can be generalized to show that #d/dxa^x = a^xln(a)# for any constant #a>0#

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