CACI SE28A
Differentiate the following functions:
1 1
1. (i) x3 (i1) 2. (1) () (i0)3x
3. (i) 3x-5 () (ii) 6-/2
5x
(ü) 5x-3/2 4
4. (i) 6x+ 4r°-3x+ 2x -7 +
(iii) ax + bx + cX + d, where a, b, c, d are constants
5. (i) 4x° + 3-2 +6-/x +5cot x
3 - + * ' +6x2/3_6
3
2 3 6cot x
6. (i) 4cot x cos X+ + +9
2 Sin x COsecX
(ii) 5tan x + 4tan x cos X 3 cot X sec x + 2sec X-13
7. (i) (2x + 3) (3x-5) (ü) x(1 + x)³
3
(vi)(2x* +5x -1)(x- 3)
3x+ 4x -5
8. (i) (iü).(r°+ 1)(x -2) (ii)
x4
24x
(iv) ( +x) v (v).ax+ bx+c (vi) a+ bcos x
sin x
9. (i) If y= 6x 4r- 2r+ 5x -9, find dy at x =-1.
dx
(ii) If y = (sin x + tan x), find dy at x =
dx 3
(ii) If y =(2-3cos x) find dy at x =
sin x dx 4
show that 2x dy
10.
y=(V dx
+y= 2/x.
11. Ify =|
12. If y = 1+ cos 2x find dy
prove that
a)--)
1- cos 2x dx
850 Senior Secondary School Mathematics for Class 11
13. y = 1- tan(x/2) find dy
1+ tan (x/2) dx
Hint 1- tan"(x/2) = COS X,
1+ tan (x/2)
EXERCISE 28B
Find the derivative of each of the following from the first principle:
1. (ax + b) 2.
(a) 1
3. 3x+ 2r -5
1
4. x-2x + x+ 3
5. r8 6.
3
7. 8. Jax +b
1 1 1
9. 5x-4 10. 11. 12.
x+2 /2x +3 J6x-5
1 2x + 3 5-x x²+1 X#0
13. 14. 15. 16.
/2-3x 3x + 2 5+ x
17. cos 3x 18. sec x 19. tan x 20. sin (2x + 3)
21. tan (3x + 1)
Differentiate:
1. r sin x 2. e cos X 3. e cot x
4. x" cot x 5. x'sec x 6. (x*+ 3x + 1) sin x
7. x tan x 8. (3x-5)(4x²-3 + e) 9. (r? 4x + 5)(x³-2)
10. (x+ 2x - 3)(x+7x +5) 11. (tan x + sec x)(cot x + cosec x)
12. (x° cos X 2* tan x)
Differentiate:
log x e
2. 3. 4.
(1+ x) (1+x)
5. 6.
x*+ 3x -1
7 (x*-1) 8.
5x*+ 6x +7
x+2 (x*+7x+ 1) 2x+3x +4
9. 10. 11. 12.
sin x Va -x log x
2cot x sin x 1+ sinx (1
13. 14. 15. 16.
(1+ cos x) 1- sin x 1+ coS X,
sin x - cos x sec x-tan x e+ sin x
17, 18. 19.
sin x t cOs X, sec x + tan |1+ log x
e sin X 2 cot x e (x -1)
20. 21. 22.
Sec x (x+ 1)
x tan ax +bx+c sin x-x COS X
23. 24. 25.
(sec x + tan x) px'+ qx +r) Xsin + cOs X
COS X
26. (i) cot x (ii) sec x Hint Write cot x = and sec x =
sin x COS X
