What is the derivative of $pi^x$ ?

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Answer 1 · 2016-06-26T05:06:09

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

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

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

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

(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 $a>0$

What is the derivative of pi^xpi^x?