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

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

Differentiate.

Question 1.

√x w.r.t x^{2}.

Solution:

Question 2.

sin x. w.r.t. cot x.

Solution:

Let y = sin x and z = cot x

Question 3.

\(\frac{1-\cos x}{1+\cos x}\) w.r.t \(\frac{1-\sin x}{1+\sin x}\)

Solution:

Question 4.

tan-1 x w.r.t. tan^{-1} \( \sqrt{1+x^2} \)

Solution:

Question 5.

sin^{-1} \(\left(\frac{2 x}{1+x^2}\right)\) w.r.t cos^{-1} \(\left(\frac{1-x^2}{1+x^2}\right)\)

Solution:

Let y = sin^{-1} \(\frac{2 x}{1+x^2}\) and z = cos^{-1} \(\frac{1-x^2}{1+x^2}\)

Then y = 2 tan^{-1} x and z = 2 tan^{-1} x

So y = z

∴ \(\frac{d y}{d z}\) = 1.