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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 \(f(x)=\left\{\begin{array}{l} x+1, \quad \text { when } x<2 \\ 2 x-1 \text { when } x \geq 2 \end{array}\right.\), 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 + 5x+ 3x + 7

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

  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 : \(s(t)=\sqrt[4]{\frac{t^3+1}{t^3-1}}\)

  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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