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)#