If `y=(x^2)/2+1/2xsqrt(x^2+1)+(log)_esqrt(x+sqrt(x^2+1))` , prove that `2y=x y^(prime)+(log)_e y^(prime),w h e r ey '` denotes the derivative w.r.t `xdot`

If y=(x^2)/2+1/2xsqrt(x^2+1)+1/2(log)_esqrt(x+sqrt(x^2+1)) , prove that 2y=x y^(prime)+(log)_e y^(prime),w h e r ey ' denotes the derivative w.r.t xdot

If y=(x^2)/2+1/2xsqrt(x^2+1)+1/2(log)_esqrt(x+sqrt(x^2+1)) , prove that 2y=x y^(prime)+1/2(log)_e y^(prime),w h e r ey ' denotes the derivative w.r.t xdot

If quad (x^(2))/(2)+(1)/(2)x sqrt(x^(2)+1)+log_(e)sqrt(x+sqrt(x^(2)+1))y=(x^(2))/(2)+(1)/(2)x sqrt(x^(2)+1)+log_(e)sqrt(x+sqrt(x^(2)+1)) prove that 2y=xy'+log_(e)y', where y' denotes the derivative w.r.x.

"If "y=(x^(2))/(2)+(1)/(2)xsqrt(x^(2)+1)+log_(e)sqrt(x+sqrt(x^(2)+1)), then

"If "y=(x^(2))/(2)+(1)/(2)xsqrt(x^(2)+1)+log_(e)sqrt(x+sqrt(x^(2)+1)), then

y=(x^(2))/(2)+(1)/(2)x sqrt(x^(2)+1)+ln sqrt(x+sqrt(x^(2)+1)) prove that 2y=xy'+ln y'

Find the derivatives w.r.t. x : x=y log(xy)

y=[log(x+sqrt(x^2+1))]^2 then prove that (x^2+1)y_2+x y_1=2

y=[log(x+sqrt(x^2+1))]^2 then prove that (x^2+1)y_2+x y_1=2