Question

If `y=sqrtx+1/sqrtx` then prove that `2x (dy)/(dx)+y=2sqrtx`

Answer 1

`y=sqrtx+(1)/(sqrtx)rArrsqrtxy=x+1" ...(i)"`
On differentiating both sides of (i) w.r.t. x, we get
`sqrtx.(dy)/(dx)y.(1)/(2)x^(-1//2)=1`
`rArrsqrtx(dy)/(dx)+(y)/(2sqrtx)=1`
`rArr 2x(dy)/(dx)+y=2sqrtx.`