Odisha State Board Elements of Mathematics Class 12 CHSE Odisha Solutions Chapter 7 Continuity and Differentiability Ex 7(g) Textbook Exercise Questions and Answers.

## CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Exercise 7(g)

Find \(\frac{d y}{d x}\)

Question 1.

xy^{2} + x^{2}y + 1 = 0

Solution:

xy^{2} + x^{2}y + 1 = 0

Question 2.

\(x^{\frac{1}{2}} y^{-\frac{1}{2}}\) + \(x^{\frac{3}{2}} y^{-\frac{3}{2}}\) = 0

Solution:

Question 3.

x^{2} + 3y^{2} = 5

Solution:

x^{2} + 3y^{2} = 5

⇒ \(\frac{d}{d x}\)(x^{2}) + 3 \(\frac{d}{d x}\)(y^{2}) = 0

⇒ 2x + 6y\(\frac{d y}{d x}\) = 0

⇒ \(\frac{d}{d x}\) = –\(\frac{x}{3 y}\)

Question 4.

y^{2} cot x = x^{2} cot y.

Solution:

y^{2} cot x = x^{2} cot y

Question 5.

y = tan xy

Solution:

y = tan xy

Question 6.

x = y In (xy).

Solution:

x = y In (xy).

Question 7.

e^{xy} + y sin x = 1

Solution:

e^{xy} + y sin x = 1

Question 8.

In \(\sqrt{x^2+y^2}\) = tan^{-1 }\(\frac{y}{x}\)

Solution:

Question 9.

y^{x} = x^{sin }^{y}

Solution:

y^{x} = x^{sin }^{y}

Question 10.

If sin (x + y) = y cos (x + y) then prove that \(\frac{d y}{d x}\) = –\(\frac{1+y^2}{y^2}\).

Solution:

Question 11.

If \(\sqrt{1-x^4}\) + \(\sqrt{1-y^4}\) = k(x^{2} – y^{2}) then show that \(\frac{d y}{d x}\) = \(\frac{x \sqrt{1-y^4}}{y \sqrt{1-x^4}}\).

Solution: