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KCET2015MathematicsDifferentiation

If ( P = | array ll x & 1 1 & x array | ) and ( Q = | array lll x & 1 & 1 1 & x & 1 1 & 1 & x array | ),then ( d Q d x = )

Options

  1. A( 3 P+1 )
  2. B( 1-3 P )
  3. C( -3 P )
  4. D( 3 P )

Correct answer

D. ( 3 P )

Step-by-step solution

Given that ( P= | array ll x & 1 1 & x array |, Q= | array lll x & 1 & 1 1 & x & 1 1 & 1 & x array | ) So, ( P=x²-1 ) And ( Q=x (x²-1 )-(x-1)+(1-x) ) ( =x³-3 x+2 ) Now, ( d Q d x =3 x²-3 ) ( =3 (x²-1 )=3 P )

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