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If y sqrt(1+ x ^(2)) = log ( x + sqrt( 1...

If `y sqrt(1+ x ^(2)) = log ( x + sqrt( 1 + x ^(2)))` then ` (1 + x ^(2)) y_(1) + xy=`

A

1

B

0

C

2

D

`-1`

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A
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DIPTI PUBLICATION ( AP EAMET)-DIFFERENTIATION -EXERCISE 1D
  1. If y =a cos (log x) + b sin (log x) then x ^(2) y (2) + xy (1)+y=

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  2. Cos^(-1) ((y)/(b)) =2 log "" ((x)/(2)) , x gt 0 implies x ^(2) (a ^(2)...

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  3. If y sqrt(1+ x ^(2)) = log ( x + sqrt( 1 + x ^(2))) then (1 + x ^(2))...

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  4. If y = ae ^(-bx) cos (cx +d) then y (2) + 2by(1) + (b ^(2) +c ^(2)) y...

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  5. If y = ax ^(n+1)+ bx ^(-n) then x ^(2) y (2) =

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  6. If y = ae ^(nx) + be ^(-nx) then y (2)=

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  7. If y = e ^(-kx //2) (a cos nx + b sin nx) then y (2)+ky(1)+ (n^(2) + k...

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  8. If y =a cos (sin x) + b sin (sin x) then y (2) + (tan x) y(1)=

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  9. f (x) = 10 cos x + (13 + 2x) sin x implies f''(x) + f(x) =

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  10. If ay ^(4) = (x+ b) ^(5) then 5 y y(2)=

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  11. If ax ^(2) + by ^(2) =c, then y (2) =

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  12. If x ^(2) + xy + y ^(2) = a ^(2), then y (2) =

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  13. If x ^(3) + y ^(3) = 3axy then y (2) =

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  14. If y ^(2) = (x-a)(x-b)then ( d ^(3))/(dx ^(3)) [((d ^(2) y)/(dx ^(2))^...

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  15. If x ^(3) + y^(3) = 3ax ^(2) then y (2)=

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  16. If y ^(2) = a ^(2) cos ^(2) x + b b^(2) sin ^(2) x then y + y (2)=

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  17. If ax ^(2) + 2hxy + by ^(2) =1 then (hx + by) ^(3) y (2) =

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  18. If x ^(3) - 3ax ^(2) + y ^(3) =0then y ^(5) y (2) =

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  19. If x ^(2) + y ^(2) =a ^(2) then ((1+ y (1) ^(2))^(3//2))/(|y(2)|)=

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  20. If y ^(2) = 4ax then 4a^2 (1+ y(1) ^(2)) ^(3//2) + (y ^(2) + 4a ^(2))...

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