What's the derivative of $arctan(8^x)$ ?

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Answer 1 · 2016-04-15T03:12:26

$(8^x ln 8)/(1+8^(2x))$

Let u = $8^x=e^(x ln 8) and y = arc tan 8^x$ .
$d/dx(y)=d/du(y)d/dx(u)$ .
$=1/(1+u^2)(ln 8 e^(x ln 8))$
$= (8^x ln 8)/(1+8^(2x))$

What's the derivative of arctan(8^x)arctan(8^x)?