Verified answer

 y = x   ⁄   [ 2√(441 – 42x)  ] ... take out the (1 ⁄ 2) and put it back later

 y = x • (441 – 42x)^(-½) ... use the product rule

 y ' = x  •  (-½) (- 42) (441 – 42x)^(- 3 ⁄ 2) + (441 – 42x)^(-½)

 y ' = (441 – 42x)^(-½) • [ 21x  •  (441 – 42x)^(- 3 ⁄ 2)  +  1 ]

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Use nested product rules to get the 2nd derivative. It's ugly.

      Term 1 = (441 – 42x)^(-½)

   d{Term 1} ⁄ dx = 21 •  (441 – 42x)^(- 3 ⁄ 2)

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    Term 2 = -  21x  •  (441 – 42x)^(- 3 ⁄ 2)  +  1

 d{Term 2} ⁄ dx = (1323) •  x  •  (441 – 42x)^(- 5 ⁄ 2)  +  -  21  •  (441 – 42x)^(- 3 ⁄ 2)

 d{Term 2} ⁄ dx = 21•  (441 – 42x)^(- 3 ⁄ 2) • [ (63) •  x  •  (441 – 42x)^(- 1)  –  1 ]

 d{Term 2} ⁄ dx = 21•  (441 – 42x)^(- 3 ⁄ 2) • [ (63) •  x ⁄ (441 – 42x)   –   1 ]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

y ' ' = (441 – 42x)^(-½) • 21•  (441 – 42x)^(- 3 ⁄ 2) • [ (63) •  x ⁄ (441 – 42x)   –   1 ]

   +  [ 21x  •  (441 – 42x)^(- 3 ⁄ 2)  +  1 ] • 21 •  (441 – 42x)^(- 3 ⁄ 2)

... add the (one- half) back.

y ' ' = (½) • {{ (441 – 42x)^(-½) • 21•  (441 – 42x)^(- 3 ⁄ 2) • [ (63) •  x ⁄ (441 – 42x)   – 1 ]

   +  [ 21x  •  (441 – 42x)^(- 3 ⁄ 2)  +  1 ] • 21 •  (441 – 42x)^(- 3 ⁄ 2) }}

You can factor this further if necessary.