Dr.Harswaroop Sharma Mathematics Solution Class 12 Chapter 5 सांतत्य तथा अवकलनीयता (Continuity and Differentiability) Exercise 5C

निम्न फलनों का $x$ के सापेक्ष अवकलन कीजिए :

Question 1

1. (i) $\sin ^{-1} a x$

(ii) $\cos ^{-1} \frac{x}{a}$

(iii) $\cos ^{-1} \frac{2 x}{5}$

(iv) $\sin ^{-1} 2 x$

Question 2

2. (i) $\log _e \tan ^{-1} x$
(ii) $\log _e \sin ^{-1} x$

Question 3

3. (i) $\sec \left(\tan ^{-1} x\right)$
(ii) $\cos \left(a \sin ^{-1} \frac{1}{x}\right)$
(iii) $\cot \left(\cos ^{-1} x\right)$

Question 4

4. (i) $\tan ^{-1} \sqrt{x}$
(ii) $\sec ^{-1} x^2$
(iii) $\operatorname{cosec}^{-1} \sqrt{x}$

Question 5

5. (i) $\tan ^{-1}\left(\frac{\sin x+\cos x}{\cos x-\sin x}\right)$
(ii) $\tan ^{-1}\left(\frac{1+\tan x}{1-\tan x}\right)$

Question 6

6. (i) $\sin ^{-1}\left(\frac{2 x}{1+x^2}\right)$
(ii) $\sin ^{-1}\left[\frac{1-x^2}{1+x^2}\right], 0<x<1$

Question 7

7. (i) $x \tan ^{-1} x$
(ii) $\left(\sin ^{-1} x\right)(\log x)$
(iii) $\left(\sin ^{-1} x\right)^m \cdot\left(\cos ^{-1} x\right)^n, 0<x<1$

Question 8

8. $\cos ^{-1}\left[e^{\sqrt{\tan x}}\right]$

Question 9

9. $\sin ^{-1} x+\sin ^{-1} \sqrt{1-x^2}$

Question 10

10. $\tan ^{-1}\left[\frac{x}{a}+\tan ^{-1} \frac{x}{a}\right]$

Question 11

11. $\sin ^{-1} \sqrt{1-x}+\cos ^{-1} \sqrt{x}$

Question 12

12. $\sin ^{-1}\left(e^{\tan ^{-1} x}\right)$

Question 13

13. $\log _e\left(\sin ^{-1} x^2\right) \cdot \cos \left(\cot ^{-1} x^2\right)$

Question 14

14. $e^{a x} \sin ^{-1} b x$

Question 15

15. $\sec ^{-1} \cdot \frac{x+1}{x-1}+\sin ^{-1} \frac{x-1}{x+1}$

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