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RBSE Solutions for Class 12 Maths Chapter 7 Differentiation Ex 7.5

June 7, 2019 by Fazal Leave a Comment

Rajasthan Board RBSE Class 12 Maths Chapter 7 Differentiation Ex 7.5

Question 1.
RBSE Solutions for Class 12 Maths Chapter 7 Differentiation Ex 7.5
(i) y = x3 + tan x
(ii) y = x2 + 3x + 2
(iii) y = x cos x
(iv) y = 2 sin x + 3 cos x
(v) y = e-x cos x
(vi) y = a sin x – b cos x
Solution:
(i) y = x3 + tan x
Diff. w.r.t. x on both
RBSE Solutions for Class 12 Maths Chapter 7 Differentiation Ex 7.5
Again diff. w.r.t. x on both sides
RBSE Solutions for Class 12 Maths Chapter 7 Differentiation Ex 7.5

(ii) y = x2 + 3x + 2
Diff. w.r.t. x on both sides,
RBSE Solutions for Class 12 Maths Chapter 7 Differentiation Ex 7.5

(iii) y = x cos x
Diff. w.r.t. x on both sides,
RBSE Solutions for Class 12 Maths Chapter 7 Differentiation Ex 7.5

(iv) y = 2 sin x + 3 cos x
Diff. w.r.t. x on both sides,
RBSE Solutions for Class 12 Maths Chapter 7 Differentiation Ex 7.5
RBSE Solutions for Class 12 Maths Chapter 7 Differentiation Ex 7.5

(v) y = e-ex cos x
Diff. w.r.t. x on both sides,
RBSE Solutions for Class 12 Maths Chapter 7 Differentiation Ex 7.5

(vi) y = a sin x – b cos x
Diff. w.r.t. x on both sides,
RBSE Solutions for Class 12 Maths Chapter 7 Differentiation Ex 7.5

Question 2.
If y = a sin x + b cos x, then prove that:
RBSE Solutions for Class 12 Maths Chapter 7 Differentiation Ex 7.5
Solution:
Given
y = a sin x + b cos x …..(i)
Diff. w.r.t. x on both sides,
RBSE Solutions for Class 12 Maths Chapter 7 Differentiation Ex 7.5

Question 3.
If y = sec x + tan x, then prove that:
RBSE Solutions for Class 12 Maths Chapter 7 Differentiation Ex 7.5
Solution:
Given y = sec x + tan x
Diff. w.r.t. x on both sides,
RBSE Solutions for Class 12 Maths Chapter 7 Differentiation Ex 7.5
RBSE Solutions for Class 12 Maths Chapter 7 Differentiation Ex 7.5

Question 4.
If.y = a cos nx + b sin nx, then prove that:
RBSE Solutions for Class 12 Maths Chapter 7 Differentiation Ex 7.5
Solution:
Given
y = A cos nx + b sin nx
Diff. w.r.t. x on both sides,
RBSE Solutions for Class 12 Maths Chapter 7 Differentiation Ex 7.5

Question 5.
If x = a cos3 θ, y = a sin3 θ, then find \(\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \) at θ = \(\frac { \pi }{ 4 } \)
Solution:
Given y = a sin3 θ
and x = a cos3 θ
Diff. w.r.t. θ on both sides,
RBSE Solutions for Class 12 Maths Chapter 7 Differentiation Ex 7.5
RBSE Solutions for Class 12 Maths Chapter 7 Differentiation Ex 7.5

Question 6.
If x3 + y3 – 3axy = 0, then prove that
RBSE Solutions for Class 12 Maths Chapter 7 Differentiation Ex 7.5
Solution:
Given,
x3 + y3 – 3axy = 0
Diff. w.r.t x on both sides,
RBSE Solutions for Class 12 Maths Chapter 7 Differentiation Ex 7.5
RBSE Solutions for Class 12 Maths Chapter 7 Differentiation Ex 7.5

Question 7.
If y = sin-1 x, then prove that:
RBSE Solutions for Class 12 Maths Chapter 7 Differentiation Ex 7.5
Solution:
Given
y = sin-1 x
Diff. w.r.t. x on both sides
RBSE Solutions for Class 12 Maths Chapter 7 Differentiation Ex 7.5

Question 8.
If y = (sin-1 x)2, then prove that:
RBSE Solutions for Class 12 Maths Chapter 7 Differentiation Ex 7.5
Solution:
Given y = (sin-1 x)2
Diff. w.r.t. x on both sides,
RBSE Solutions for Class 12 Maths Chapter 7 Differentiation Ex 7.5

RBSE Solutions for Class 12 Maths

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