Question 1140604
the derivative of 

{{{y = r / sqrt(r^2 + 1 )}}}


{{{(d/dr) ( r / sqrt(r^2 + 1 ))}}}=

Apply the Quotient Rule :

{{{(f/g)'= (f'*g-g'*f)/g^2 }}}


= {{{((d/dr)(r)sqrt(r^2+1)-(d/dr)(sqrt(r^2+1))r)/(sqrt(r^2+1)^2)}}}....since {{{(d/dr)(r)=1}}} and {{{(d/dr)(sqrt(r^2+1)) =r / sqrt(r^2 + 1 )}}} , we have


= {{{(sqrt(r^2+1)-(r / sqrt(r^2 + 1 ))r)/(sqrt(r^2+1)^2)}}}

 

Simplify : {{{ (sqrt(r^2+1)-(r/sqrt(r^2+1))r)/(sqrt(r^2+1)^2)}}}: you will get


={{{1/((r^2+1)sqrt(r^2+1)) }}}


or


={{{1/sqrt((r^2+1)^3) }}}


or


={{{1/(r^2+1)^(3/2) }}}