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RBSE Solutions for Class 12 Maths Chapter 7 अवकलन Ex 7.1

May 9, 2019 by Fazal 1 Comment

RBSE Solutions for Class 12 Maths Chapter 7 अवकलन Ex 7.1 is part of RBSE Solutions for Class 12 Maths. Here we have given Rajasthan Board RBSE Class 12 Maths 7 अवकलन Exercise 7.1.

Rajasthan Board RBSE Class 12 Maths Chapter 7 अवकलन Ex 7.1

प्रश्न 1.
sin (x²)
हल :
माना कि y = Sin (x²)
x के सापेक्ष अवकलन करने पर
RBSE Solutions for Class 12 Maths Chapter 7 अवकलन Ex 7.1 1
= cos (x²) 2x
= 2x cos (x²)

प्रश्न 2.
tan (2x + 3)
हल :
माना कि y = tan (2x + 3)
x के सापेक्ष अवकलन करने पर
RBSE Solutions for Class 12 Maths Chapter 7 अवकलन Ex 7.1 2
= sec² (2x + 3)\(\frac { d }{ dx }\)(2x + 3)
= sec² (2x + 3).(2 x 1 + 0)
= 2 sec² (2x + 3).

प्रश्न 3.
sin {cos (x²)}
हल :
माना कि y = sin {cos (x²)}
x के सापेक्ष अवकलन करने पर
RBSE Solutions for Class 12 Maths Chapter 7 अवकलन Ex 7.1 3
= cos (cos x²) \(\frac { d }{ dx }\) (cos x²)
= cos (cos x²). ( – sin x²) \(\frac { d }{ dx }\) x²
= – cos (cos x²) sin (x²).2x
= – 2x sin (x²) cos (cos x²)

प्रश्न 4.
RBSE Solutions for Class 12 Maths Chapter 7 अवकलन Ex 7.1 4
हल-
माना कि
RBSE Solutions for Class 12 Maths Chapter 7 अवकलन Ex 7.1 5
x के सापेक्ष अवकलन करने पर
RBSE Solutions for Class 12 Maths Chapter 7 अवकलन Ex 7.1 6

प्रश्न 5.
RBSE Solutions for Class 12 Maths Chapter 7 अवकलन Ex 7.1 7
हल-
माना कि
RBSE Solutions for Class 12 Maths Chapter 7 अवकलन Ex 7.1 8
x के सापेक्ष अवकलन करने पर
RBSE Solutions for Class 12 Maths Chapter 7 अवकलन Ex 7.1 9

प्रश्न 6.
sin x°
हल :
दिया है, y = sin x°
∵ 180° = π रेडियन
RBSE Solutions for Class 12 Maths Chapter 7 अवकलन Ex 7.1 10

प्रश्न 7.
RBSE Solutions for Class 12 Maths Chapter 7 अवकलन Ex 7.1 11
हल :
RBSE Solutions for Class 12 Maths Chapter 7 अवकलन Ex 7.1 12
RBSE Solutions for Class 12 Maths Chapter 7 अवकलन Ex 7.1 13

प्रश्न 8.
sec x°
हल :
दिया है, y = sec x°
हम जानते हैं कि 180° = π रेडियन
1° = रेडियन
x° = रेडियमन
RBSE Solutions for Class 12 Maths Chapter 7 अवकलन Ex 7.1 14

प्रश्न 9.
RBSE Solutions for Class 12 Maths Chapter 7 अवकलन Ex 7.1 15
हल :
माना कि
RBSE Solutions for Class 12 Maths Chapter 7 अवकलन Ex 7.1 16
RBSE Solutions for Class 12 Maths Chapter 7 अवकलन Ex 7.1 17

प्रश्न 10.
RBSE Solutions for Class 12 Maths Chapter 7 अवकलन Ex 7.1 18
हल :
माना कि
RBSE Solutions for Class 12 Maths Chapter 7 अवकलन Ex 7.1 19
x के सापेक्ष अवकलन करने पर
RBSE Solutions for Class 12 Maths Chapter 7 अवकलन Ex 7.1 20

प्रश्न 11.
RBSE Solutions for Class 12 Maths Chapter 7 अवकलन Ex 7.1 21
हल :
माना कि
RBSE Solutions for Class 12 Maths Chapter 7 अवकलन Ex 7.1 22
= loge (x² + x + 1) – loge (x² – x + 1)
x के सापेक्ष अवकलन करने पर
RBSE Solutions for Class 12 Maths Chapter 7 अवकलन Ex 7.1 23

प्रश्न 12.
RBSE Solutions for Class 12 Maths Chapter 7 अवकलन Ex 7.1 24
हल :
माना कि
RBSE Solutions for Class 12 Maths Chapter 7 अवकलन Ex 7.1 25
x के सापेक्ष अवकलन करने पर
RBSE Solutions for Class 12 Maths Chapter 7 अवकलन Ex 7.1 26

प्रश्न 13.
atan 3x
हल :
माना कि
y = atan 3x
x के सापेक्ष अवकलन करने पर
RBSE Solutions for Class 12 Maths Chapter 7 अवकलन Ex 7.1 27

प्रश्न 14.
loge (sec x + tan x).
हल :
माना कि
y = loge (sec x + tan x)
x के सापेक्ष अवकलन करने पर
RBSE Solutions for Class 12 Maths Chapter 7 अवकलन Ex 7.1 29
= sec x

प्रश्न 15.
sin³x • sin 3x.
हल :
माना कि
y = sin3 x . sin 3x
= sin3 x[3 sin x – 4 sin3 x]
[∵ sin 3θ = 3sin θ – 4 sin3 θ]
y = 3 sin4 x – 4 sin6 x
x के सापेक्ष अवकलन करने पर
RBSE Solutions for Class 12 Maths Chapter 7 अवकलन Ex 7.1 30
= 12 sin3x . cos x – 24 sin5 x cos x
= 12 sin3x cos x (1 – 2 sin2 x)
= 12 sin3x cos x . cos 2x
= 6 sin2 x . 2 sin x . cos x . cos 2x
= 6 sin2x . sin 2x · cos 2x
= 3 sin2x . 2 sin 2x . cos 2x
= 3 sin2x sin 2(2x)
= 3 sin2x . sin 4x.

We hope the given RBSE Solutions for Class 12 Maths Chapter 7 अवकलन Ex 7.1 will help you. If you have any query regarding RBSE Solutions for Class 12 Maths Chapter 7 अवकलन Ex 7.1, drop a comment below and we will get back to you at the earliest.

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