If fx = x - 2 + x + 

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 Multiple Choice QuestionsMultiple Choice Questions

111.

If x2 + y2t - 1t and x4 + y4t2 + 1t2, then dydx

  • 1x2y3

  • 1xy3

  • 1x2y2

  • 1x3y


112.

If y = sec-1cscx + csc-1secx + sin-1cosx + cos-1sinx, then dydx is equal to

  • 0

  • 2

  • - 2

  • - 4


113.

If y = ex . ex2 . ex3 . ... exn ..., for 0 < x < 1, then dydx at x = 12 is

  • e

  • 4e

  • 2e

  • 3e


114.

The derivative of tan-12x1 - x2 with repsect to cos-11 - x2 is

  • 1 - x21 + x2

  • 11 - x2

  • 21 - x21 + x2

  • 21 - x21 + x2


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115.

Let f(x) = ex - 12sinxalog1 + x4 for x  0 and f(0) = 12.  If f is continuous at x = 0, then the value of a is equal to

  • 1

  • - 1

  • 2

  • 3


116.

If y = sin-11 - x, then dydx is equal to

  • 11 - x

  • - 121 - x

  • 1x

  • - 12x1 - x


117.

The derivative of sin-12x1 - x2 with respect to sin-13x - 4x is

  • 23

  • 32

  • 12

  • 1


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118.

If fx = x - 2 + x + 1 - x, then f'- 10 is equal to

  • - 3

  • - 2

  • - 1

  • 0


A.

- 3

For x < - 1, the given function is

f(x) = 2 - x - x - 1 - x

      = 1 - 3x

        f'(x) = - 3 f'(- 10) = - 3


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119.

If x = a1 + cosθ, y = aθ + sinθ, then d2ydx2 at θ = π2 is

  • 1a

  • 1a

  • - 1

  • - 2


120.

If y = tan-1cosx1 + sinx, then dydx is equal to

  • 12

  • 2

  • - 2

  • 12


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