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 x2.
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.