RBSE Solutions for Class 12 Maths Chapter 7 Differentiation Ex 7.5

Rajasthan Board RBSE Class 12 Maths Chapter 7 Differentiation Ex 7.5

Question 1.

(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

Again diff. w.r.t. x on both sides

(ii) y = x² + 3x + 2
Diff. w.r.t. x on both sides,

(iii) y = x cos x
Diff. w.r.t. x on both sides,

(iv) y = 2 sin x + 3 cos x
Diff. w.r.t. x on both sides,

(v) y = e^-ex cos x
Diff. w.r.t. x on both sides,

(vi) y = a sin x – b cos x
Diff. w.r.t. x on both sides,

Question 2.
If y = a sin x + b cos x, then prove that:

Solution:
Given
y = a sin x + b cos x …..(i)
Diff. w.r.t. x on both sides,

Question 3.
If y = sec x + tan x, then prove that:

Solution:
Given y = sec x + tan x
Diff. w.r.t. x on both sides,

Question 4.
If.y = a cos nx + b sin nx, then prove that:

Solution:
Given
y = A cos nx + b sin nx
Diff. w.r.t. x on both sides,

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,

Question 6.
If x³ + y³ – 3axy = 0, then prove that

Solution:
Given,
x³ + y³ – 3axy = 0
Diff. w.r.t x on both sides,

Question 7.
If y = sin^-1 x, then prove that:

Solution:
Given
y = sin^-1 x
Diff. w.r.t. x on both sides

Question 8.
If y = (sin^-1 x)², then prove that:

Solution:
Given y = (sin^-1 x)²
Diff. w.r.t. x on both sides,

RBSE Solutions for Class 12 Maths