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 x^{3} + y^{3} = t – \(\frac { 1 }{ t } \) and x^{6} + y^{6} = t^{2} + \(\frac { 1 }{ { t }^{ 2 } } \) then prove that x^{4}y^{2} \(\frac { dy }{ dx } \) = 1

Solution:

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