y = x/2 * [ (441 - 42 x) ^(1/2)]
so,
dy/dx = 1/2 * [(441 - 42 x)^.5] + x/2 * [ (1/2) (441-42x)^(-1/2) d/dx (441-42x)
= 1/2 * [(441 - 42 x)^.5] + x/2 * [ (1/2) (441-42x)^(-1/2) (-42)]
= 1/2 * [(441 - 42 x)^.5] - 42x/4 * [ 1 / (441-42x)^(1/2) ]
= 1/2 * [(441 - 42 x)^.5] - 21x/2 * [ 1 / (441-42x)^(1/2) ]
= 1/2 [ (441 - 42 x- 21 x) / (441-42x)^.5]
= 1/2 [ 441- 63x) / (441-42x)^(.5)]
dy/dx = 3 (7-x) / [ 2 sqrt { (21-2x)/21}]..................i
&
d2y/dx^2= 3 (sqrt 21) (x-14) / 2*[(21-2x)^(3/2)]
= 1
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Verified answer
y = x/2 * [ (441 - 42 x) ^(1/2)]
so,
dy/dx = 1/2 * [(441 - 42 x)^.5] + x/2 * [ (1/2) (441-42x)^(-1/2) d/dx (441-42x)
= 1/2 * [(441 - 42 x)^.5] + x/2 * [ (1/2) (441-42x)^(-1/2) (-42)]
= 1/2 * [(441 - 42 x)^.5] - 42x/4 * [ 1 / (441-42x)^(1/2) ]
= 1/2 * [(441 - 42 x)^.5] - 21x/2 * [ 1 / (441-42x)^(1/2) ]
= 1/2 [ (441 - 42 x- 21 x) / (441-42x)^.5]
= 1/2 [ 441- 63x) / (441-42x)^(.5)]
dy/dx = 3 (7-x) / [ 2 sqrt { (21-2x)/21}]..................i
&
d2y/dx^2= 3 (sqrt 21) (x-14) / 2*[(21-2x)^(3/2)]
= 1