What is the derivative of $y=pi^x+x^pi$ ?

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Answer 1 · 2016-09-29T05:04:29

$y' = ln(pi)*x^pi + pix^(pi-1)$

$y=pi^x+x^pi$

Let's split this into two: $y = y_1=pi^x$ plus $y_2 =x^pi$

$lny_1= xlnpi$

$:.y_1' = lnpi * x^pi$

$y_2' = pix^(pi-1)$ By Power rule

Now: $y' = y_1' + y_2'$

Hence: $y' = ln(pi)*x^pi + pix^(pi-1)$

What is the derivative of y=pi^x+x^piy=pi^x+x^pi?