## Rajasthan Board RBSE Class 12 Maths Chapter 7 Differentiation Ex 7.3

**Find \(\frac { dy }{ dx } \) of following functions :**

Question 1.

(i) 2x + 3y = sin y

(ii) x^{2} + xy + y^{2} = 200

Solution:

(i) 2x + 3y- sin y

Diff. w.r.t. x on both sides,

(ii) x2 + xy + y2 = 200

Diff. w.r.t. x on both sides,

Question 2.

(i) \(\sqrt { x }\) + \(\sqrt { y }\) = \(\sqrt { a }\)

(ii) tan (x + y) + tan (x – y) = 4

Solution:

(i) \(\sqrt { x }\) + \(\sqrt { y }\) = \(\sqrt { a }\)

DifF. w.r.t. x on both sides,

(ii) tan (x + y) + tan (x – y) = 4

DifF. w.r.t. x on both sides,

Question 3.

(i) sin x + 2 cos^{2} y + xy = 0

(ii)x \(\sqrt { y }\) + y\(\sqrt { x }\) = 1

Solution:

(i) sin x + 2 cos^{2} y + xy = 0

DifF. w.r.t. x on both sides,

(ii) x\(\sqrt { y }\) + y\(\sqrt { x }\) = 1

DifF. w.r.t. x on both sides,

Question 4.

(i) (x^{2} + y^{2})^{2} = xy

(ii) sin (xy) + \(\frac { x }{ y } \) = x^{2} – y

Solution:

(i) (x^{2} + y^{2}) = xy

Diff. w.r.t. x on both sides,

(ii) sin (xy) + \(\frac { x }{ y } \) = x^{2} – y

Diff. w.r.t. x on both sides,

Question 5.

(i) x^{3} + y^{3} = 3axy

(ii) x^{y} + y^{x} = ab

Solution:

(i) x^{3} + y^{3} = 3axy

DifF. w.r.t. x on both sides,

(ii) x^{y} + y^{x} = ab

Solution :

Let u = x^{y} and v = y^{x}

Then, u + v = a^{b}

Again, u = x^{y} and v = y^{x}

Taking log on both sides,

log u = y log x and log v = x log y

DifF. w.r.t. x,

Question 6.

(i) y = x^{y}

(ii) x^{a }. y^{b} = (x – y)^{a+b}

Solution:

(i) y = x^{y}

Taking log on both sides,

log y = log x^{y} = y log x

Diff. w.r.t. x on both sides,

Question 7.

Solution:

Question 8.

Solution:

Question 9.

Solution:

Question 10.

Solution:

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