How do you differentiate $r/(r^2 + 1)^(1/2)$ ?

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Answer 1 · 2018-05-05T17:30:35

$f'(r)=1/((r^2+1)^(3/2)$

Here,

$f(r)=r/sqrt(r^2+1)$

$"Using "color(blue)"Quotient Rule:"$ ,w.r.t. $r$

$f'(r)=(sqrt(r^2+1)d/(dr)(r)-rd/(dr)(sqrt(r^2+1)))/(sqrt(r^2+1))^2$

$=(sqrt(r^2+1)(1)-rxx1/(cancel2sqrt(r^2+1))(cancel2r))/(r^2+1)$

$=(r^2+1-r^2)/((r^2+1)sqrt(r^2+1))$

$f'(r)=1/((r^2+1)^(3/2)$

How do you differentiate r/(r^2 + 1)^(1/2)r/(r^2 + 1)^(1/2)?