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

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

Discussion

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