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Physics Wallah Study Material

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BATCH CODE: \

Physics Wallah

SUBJECT NAME: MATHS

CHAPTER NAME:
Method of Differentiation

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2. O

[topic] Method of Differentiation

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3. &

Let .
y(x) = (1+ x)(1 +x7)(1 + x*)(1 + x®)(1 + x79). peer eee *E
Then y' — y” atx= 1 —1 is equal to

id ey UN ge
(a (ex 04x). -- Gr) tase) 3 u

976 A
[a) Eny © er Feen

464 Ale wre ay) 6-16 ==
EN (ya yC9 = ETS LY = ser]
Ra xe! eb A (>)
A... a: u)

y AG cere at

4. If y(x) = x*,x > 0, then y”'(2) — 2y'(2) is equal to:

EN Blog, 2 — 2
EX 4loge 2 +2
| foo 272—2
EX 4(log. 2)? +2

x

=
q = (Va hor)

fours

j - (oad) aC Im) x Mw)

pe tz
Jere 4G) HH) à

= 2 + (Cta hw) y

&

LL

Mgt) = Haye
re

Now)

db)->46)

= 2404 bm} yg (utm)
2 4 41109] iHm 2

Td: 24 (4H) (Im -1)
=2+ (a1)

=2AW hee U

5. Caussnon) mo 0
ETS nie A d

Let f(x) be a penal function such that f(x) + f’(x) + f(x) = x5 + 64. Then,

the value oflimy 1 2 2 fo Me dite | —O
- Ser tan fe de print

Eg : AMA

ee: eb. Im | for a cena thre sat
ai + A |
[A o en a Ela m4 Fo = 20 —@
[c.) pan Erro) c a Foss Mo box -O
60 GO»

EX por (We Der. aX
E {Go DE ar OS de Yo

6. Let f:S > S where S = (0,00) be a twice differentiable function such that
f(x + 1) = xf(x). If g:S > R be defined as g(x) = log, f(x), then the value of
Ig”(5) — g’’(1)| is equal to :

À n 23

ge EG) RS = "ir

B= Ink Geo ho +}nGen) à EPO) aie

De omo | a te

144 de) 00)= by qa- N ty =.
[c) 144 F60-302

[p.)> A EE

= b4 los
MITT ALY = E Rn es

y

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7. 6

Let f be a polynomial function such that f(3x) = f'(x) - f'"(x), for all x € R. Then
hs
2 fake NE
24m A iia we E paloma
£ (N: z x- da x Ale
¿ma Lto os Lx + 00d
f@)— f'(2) + f"(2) = 10 4
ala ur) <G)+ À = [SS de
[B.) f"(2)-fQ)=4 *
239 Ra

’ 9b- Car+frab| re = 44 ac
Bros. (6;
2

4b= Igab JE

b= 3b E29
Boron (ute LE

A rbe

e e

8. Ans: €

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9. 1, ifx>0
If y = cos”? cos(|x| — f (x)), where f(x) = $-1, ifx <0, then ie _ sm
0, ifx=0
Tm Md of 7 = of |
u
-1

alo) =
al le) ce
0 ++
el
M

Indeterminate

10. Ans: B

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11. AAA

If f(x) = cor (=

er

| es
(25)
BB |
ee eee

® ». ~ ECS)
Y w
Ae

), then f’(1) is equal to

| CA bev)
Fos

Fe 2 (y+)
2.

ei Me +m

12. Ans: A

6

13. fi) =x+ 1 f (50) f"(50'
E then LO) is

14. Ans: 1

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15. ®

Ifx™.y" = (x+y)"*", then 2 = MANI ds
{ory h
B z La no a ul PE SÓ
E tay a 7 GT
[B.) u Anv + = bales y) MES NA
[c\ y valor any = (nal y) 3 = +
[D.) x no. Gave KR
BE 2
Y. I > = (+
BER = ds =
% Re wen

16. YN
#Q. Let f(x) be a polynomial function of second degree if f(1) = f(-1) @
anda,b,c areinA.P. then f (a), f(b), f(c) are in

(A) AP
(B) GP
(©) HP

(D) AGP

17. f: (-1, 1) > R be a differentiable function with f(0) = -1 and f(0) = 1.
Let g(x) = (f(2f(x)+2))*, then g’(0) =?

18. Ans: -4

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19. Given, x = 2t? & y = 4t, then find ay,
dx?

20. #Q. Ifx = 3tan t and y = 3sec t, then the value of at t= Tis
[2019 Main, 9 Jan II]

Ir

(a) =
BD =
O xs
DM) =

à

21. +.
#0. Ifx= poto pe x > 0 then find 2

22. Find Y
> at (0,0). if Y =——=3—
1+ :

23. ©

° DPP

DPP NO Question No

* Module
- Exercise Name

Module Page No Question No

24. O
(enopnama
=

1. Sub Top

Method of Differentiation

Questions

&

25. 6

Solve the DPP and
check Solution

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