Students can Download Maths Chapter 5 Continuity and Differentiability Ex 5.3 Questions and Answers, Notes Pdf, 2nd PUC Maths Question Bank with Answers helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.

## Karnataka 2nd PUC Maths Question Bank Chapter 5 Continuity and Differentiability Ex 5.3

### 2nd PUC Maths Continuity and Differentiability NCERT Text Book Questions and Answers Ex 5.3

Find \(\frac{\mathrm{d} y}{\mathrm{d} x}\) in the following

Question 1.

2x + 3y = sin x

Answer:

Question 2.

2x + 3y = sin y

Answer:

Question 3.

ax + by^{2} = cos y

Answer:

Question 4.

xy + y^{2} = tan x + y

Answer:

Question 5.

x^{2} + xy + y^{2} = 100

Answer:

Question 6.

x^{3} + x^{2}y + xy^{2} + y^{3} = 81

Answer:

Question 7.

sin^{2}y + cos xy = π

Answer:

Question 8.

sin^{2} x + cos^{2} y = 1

Answer:

Question 9.

\(y=\sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right)\)

Answer:

Question 10.

\(y=\tan ^{-1}\left(\frac{3 x-x^{3}}{1-3 x^{2}}\right),-\frac{1}{\sqrt{3}}<x<\frac{1}{\sqrt{3}}\)

Answer:

Question 11.

\(y=\cos ^{-1}\left(\frac{1-x^{2}}{1+x^{2}}\right), 0<x<1\)

Answer:

Question 12.

\(y=\sin ^{-1}\left(\frac{1-x^{2}}{1+x^{2}}\right), 0<x<1\)

Answer:

Question 13.

\(y=\cos ^{-1}\left(\frac{2 x}{1+x^{2}}\right),-1<x<1\)

Answer:

Question 14.

\(y=\sin ^{-1}(2 x \sqrt{1-x^{2}}),-\frac{1}{\sqrt{2}}<x<\frac{1}{\sqrt{2}}\)

Answer:

Question 15.

\(y=\sec ^{-1}\left(\frac{1}{2 x^{2}-1}\right), 0<x<\frac{1}{\sqrt{2}}\)

Answer: