What is the derivative of $Arctan(sqrt(5x))$ ?

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Answer 1 · 2018-05-07T17:14:13

the answer
$d/dx[Arctan(sqrt(5x))]=[5/(2sqrt5x)]/[1+5x]=sqrt(5)/(2sqrt(x)*(5x+1))$

note that

$d/dx[arctan(u)]=((du)/dx)/[1+u^2]$

now let's derive $Arctan(sqrt(5x))$

$d/dx[Arctan(sqrt(5x))]=[5/(2sqrt5x)]/[1+5x]=sqrt(5)/(2*sqrt(x)*(5*x+1))$

What is the derivative of Arctan(sqrt(5x))Arctan(sqrt(5x))?