#### 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 ${dy\over dx}={sin^2(a+y)\over sin \ a}, a\neq n \pi.$