Differentiation — CBSE Class 12 board PYQs

61 past board questions on Differentiation, arranged like the paper itself — objective first, long answers last, newest year first in each section. Open any question for its complete solution.

Multiple Choice3 Qs

  1. Derivative of with respect to is:
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  2. If , then is equal to:
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  3. If , then is equal to:
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Short Answer6 Qs

  1. Find , if .
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  2. If , then find .
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  3. Differentiate with respect to .
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  4. If , find for .
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  5. If , then find .
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  6. If , prove that .
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Long Answer52 Qs

  1. If , then find .
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  2. If and , prove that .
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  3. If , find .
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  4. If and , then prove that .
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  5. Differentiate with respect to .
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  6. If , then prove that .
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  7. Differentiate with respect to .
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  8. If , find .
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  9. If and , find when .
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  10. If , prove that .
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  11. Find at if .
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  12. Differentiate the function with respect to .
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  13. If , prove that .
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  14. If and , find the values of at and .
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  15. If , prove that .
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  16. If , then find .
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  17. If , show that .
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  18. Find the value of at , if and . (2014)
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  19. If , show that . (2014)
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  20. If and , find .
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  21. If , show that .
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  22. Differentiate the following function with respect to : .
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  23. If , find .
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  24. If , prove that .
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  25. If , show that .
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  26. If , show that .
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  27. Differentiate with respect to .
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  28. If , find .
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  29. If , show that .
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  30. If , show that .
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  31. Find , if .
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  32. Find , if .
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  33. Differentiate the function with respect to .
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  34. Find if .
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  35. Differentiate the function with respect to .
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  36. Differentiate the function with respect to .
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  37. If , find .
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  38. If , find .
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  39. Differentiate the following with respect to : .
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  40. Differentiate with respect to from first principles.
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  41. If , prove that .
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  42. Differentiate with respect to from first principles.
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  43. If , show that .
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  44. If , find .
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  45. Differentiate with respect to from first principles.
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  46. If and , find .
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  47. If , find at .
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  48. If , prove that .
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  49. If and , show that .
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  50. If , find in simplified form, and also find .
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  51. If (with ), find .
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  52. If , show that .
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