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

  

प्रश्नावली - 5E

निम्नलिखित फलनों का $x$ के सापेक्ष अवकलन कीजिए-

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Question 1

1. $x^{\sin x}$.

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Question 2

2. $x^{\tan x}$.

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Question 3

3. $\frac{e^x}{\sin x}$

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Question 4

4. $(\sin x)^{\tan x}$.

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Question 5

5. $\log _e x^{\cos x}$.

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Question 6

6. $e^{\sin ^{-1} x}$.

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Question 7

7. $x^{\sin 2 x}$.

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Question 8

8. (i) $e^{x^3}$ 

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

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Question 9

9. $x^x-2^{\sin x}$

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Question 10

10. $(\log x)^x+x^{\log x}$

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Question 11

11. $\left(\sin ^{-1} x\right)^{\log _e x}$.

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Question 12

12. $(\tan x)^{\log _e x}+(\cos x)^{\sin x}$.

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Question 13

13. $(x+3)^2(x+4)^3(x+5)^4$.

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Question 14

14. $(\cos x)^y=(\cos y)^x$

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Question 15

15. $\sqrt{\frac{(x-1)(x-2)}{(x-3)(x-4)(x-5)}}$.

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Question 16

16. $\sqrt{\frac{1-x}{1+x}}$.

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Question 17

17. $(\sin x)^x+\sin ^{-1} \sqrt{x}$

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Question 18

18. $x^r+a^x+x^a$.

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Question 19

19. $x^{\sin x}+(\sin x)^{\cos x}$

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Question 20

20. $(x \cos x)^x+(x \sin x)^{1 / x}$

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Question 21

21. $(\sin x)^{\log _e x}$.

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Question 22

22. $\left(1+\frac{1}{x}\right)^x+x^{1+(1 / x)}$.

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Question 23

23. $x^{\sin x}+a^{\sin x}$.

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Question 24

24. $\cos x \cos 2 x \cos 3 x$.

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Question 25

25. $\left(x \log _e x\right)^{\log _{\log _e x} x}$.

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Question 26

26. $x^{\sin ^{-1} x}$.

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Question 27

27. $x^{x \cos x}+\frac{x^2+1}{x^2-1}$

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Question 28

28. $x^y+y^x=1$

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Question 29

29. $y^x=x^y$

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Question 30

30. यदि $y=\frac{(x+1)^2 \sqrt{x-1}}{(x+4)^3 e^x}$ तो $\frac{d y}{d x}$ का मान ज्ञात कीजिए।

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Question 31

31. यदि $y=\sqrt{\frac{1-x}{1+x}}$ तो सिद्ध कीजिए कि $\left(1-x^2\right) \frac{d y}{d x}+y=0$.

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Question 32

32. $x y=e^{x-y}$

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Question 33

33. $f(x)=(1+x)\left(1+x^2\right)\left(1+x^4\right)\left(1+x^8\right)$ द्वारा प्रदत्त फलन का अवकलज ज्ञात कीजिए और इस प्रकार $f(1)$ ज्ञात कीजिए।

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Question 34

34. निम्नलिखित फलनों का $x$ के सापेक्ष अवकलन कीजिए :
(i) $\log \left(\cos e^x\right)$
(ii) $e^x+e^{x^2}+ .......... +e^{x^5}$

(iii) $\sqrt{e^{\sqrt{x}}}$
(iv) $\log (\log x)$
(v) $\frac{\cos x}{\log x}$
(vi) $\cos \left(\log x+e^x\right)$