RBSE Solutions for Class 12 Maths Chapter 7 Differentiation Ex 7.4

RBSE Solutions for Class 12 Maths Chapter 7 Differentiation Ex 7.4 are part of RBSE Solutions for Class 12 Maths. Here we have given Rajasthan Board RBSE Solutions for RBSE Solutions for Class 12 Maths Chapter 7 Differentiation Ex 7.4.

Rajasthan Board RBSE Class 12 Maths Chapter 7 Differentiation Ex 7.4

Find \(\frac { dy }{ dx } \), if

Question 1.
(i) x = a sec t, y = b tan t
(ii) x = log t + sin t, y = e^t + cos t
Solution:
(i) x = a sec t, y = b tan t
x = a sec t
Diff. w.r.t. t on both sides,
\(\frac { dx }{ dt } \) = (a sec t) = a sec t tan t
and y = b tan t
Diff. w.r.t. t on both sides,

(ii) x = log t + sin t, y = et + cos t
x = log t + sin t
Diff. w.r.t. t on both sides,

Question 2.
(i) x = log t, y = e^t + cos t
(ii) x = a cos θ, y = b sin θ
Solution:
(i) x= log t, y = e^t + cos t
∵ x = log t
Diff. w.r.t. t on both sides,

(ii) x = a cos θ, y = b sin θ
∵ x = a cos θ
Diff. w.r.t. θ on both sides,

Question 3.
(i) x = cos θ – cos 2θ, y = sin θ – sin 2θ
(ii) x = a (θ – sin θ), y = a (1 + cos θ)
Solution:
(i) x = cos θ – cos 2θ
y = sin θ – sin 2θ
x = cos θ – cos 2θ
∵ Diff. w.r.t. θ on both sides,

(ii) x = a(θ – sin θ), y = a(1 + cos θ)
∵ x = (θ – sin θ)
Diff. w.r.t. θ on both sides,

Question 4.

Solution:

Question 5.

Solution:

Question 6.
If x³ + y³ = t – \(\frac { 1 }{ t } \) and x⁶ + y⁶ = t² + \(\frac { 1 }{ { t }^{ 2 } } \) then prove that x⁴y² \(\frac { dy }{ dx } \) = 1
Solution:

RBSE Solutions for Class 12 Maths