NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability — Exercise 5.7

Find the second order derivatives of the functions given in Exercises 1 to 10

Question 1:x2 + 3x + 2

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Question 2:x20

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Question 3:x . cos x

Question 4:log x

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Question 5:x3 log x

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Question 6:ex sin 5x

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Question 7:e6x cos 3x

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Question 8:tan–1 x

Question 9:log (log x)

Question 10:sin (log x)

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Question 11:If y = 5 cos x – 3 sin x, prove that 2 2 0

Find the second order derivatives of the functions

Question 12:If y = cos–1 x, Find 2 2 d y dx in terms of y alone.

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Question 13:If y = 3 cos (log x) + 4 sin (log x), show that x2 y2 + xy1 + y = 0

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Question 14:If y = Aemx + Benx, show that 2 2 ( ) 0 d y dy m n mny dx dx − + + =

Question 15:If y = 500e7x + 600e–7x, show that 2 2 49 d y y dx =

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Question 16:If ey (x + 1) = 1, show that 2 2 2 d y dy dx dx   =  

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Question 17:If y = (tan–1 x)2, show that (x2 + 1)2 y2 + 2x (x2 + 1) y1 = 2