Differential Calculus - Differentiability and Methods of Differentiation Book Back Questions

11th Standard

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Maths

Time : 00:45:00 Hrs
Total Marks : 30
    5 x 1 = 5
  1. If y= f(x2+2) and f'(3)=5,then \({dy\over dx}\) at x=1 is

    (a)

    5

    (b)

    25

    (c)

    15

    (d)

    10

  2. If y=mx+c and f(0)=\(f'(0)=1\),then f(2) is

    (a)

    1

    (b)

    2

    (c)

    3

    (d)

    -3

  3. \(x={1-t^2\over 1+t^2},y={2t\over 1+t^2}\) then \({dy\over dx}\)is

    (a)

    \(-{y\over x}\)

    (b)

    \({y\over x}\)

    (c)

    \(-{x\over y}\)

    (d)

    \({x\over y}\)

  4. If pv=81,then \({dp\over dv}\) at v=9 is

    (a)

    1

    (b)

    -1

    (c)

    2

    (d)

    -2

  5. If ,then f '(2) is 

    (a)

    0

    (b)

    1

    (c)

    2

    (d)

    does not exist

  6. 3 x 2 = 6
  7. Differentiate the following with respect to x: y=x3+5x2+3x+7

  8. Differentiate the following: f(t)\(=3\sqrt{1+tan \ t}\)

  9. Find the derivatives of the following If cos (xy) = x, show that \({dy\over dx}={-(1+y \ sin (xy))\over x \ sin \ xy}\)

  10. 3 x 3 = 9
  11. Determine whether the following function is differentiable at the indicated values.f(x) = x | x | at x = 0

  12. Find the derivatives of the following functions with respect to corresponding independent variables:y = ex sin x

  13. Differentiate the following:\(s(t)=\sqrt[4]{t^3+1\over t^3-1}\)

  14. 2 x 5 = 10
  15. If y = tan-1\(({1+x\over 1-x}),find \ y'\)

  16. If sin y=x sin (a+y),then prove that \({dy\over dx}={sin^2(a+y)\over sin \ a}, a\neq n \pi.\)

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