Find the second order derivatives of the functions given in Exercises 1 to 10. 1. x2 + 3x + 2 2. x20 3. x . cos x 4. log x 5. x3 log x 6. ex sin 5x 7. e6x cos 3x 8. tan1 x 9. log (log x) 10. sin (log x) 11. If y = 5 cos x 3 sin x, prove that 2 2 0 12. If y = cos1 x, Find 2 2 d y dx in terms of y alone. 13. If y = 3 cos (log x) + 4 sin (log x), show that x2 y2 + xy1 + y = 0 14. If y = Aemx + Benx, show that 2 2 ( ) 0 d y dy m n mny dx dx + + = 15. If y = 500e7x + 600e7x, show that 2 2 49 d y y dx = 16. If ey (x + 1) = 1, show that 2 2 2 d y dy dx dx = 17. If y = (tan1 x)2, show that (x2 + 1)2 y2 + 2x (x2 + 1) y1 = 2
Find the second order derivatives of the functions given in Exercises 1 to 10
Question 1:x2 + 3x + 2
Question 2:x20
Question 3:x . cos x
Question 4:log x
Question 5:x3 log x
Question 6:ex sin 5x
Question 7:e6x cos 3x
Question 8:tan–1 x
Question 9:log (log x)
Question 10:sin (log x)
Question 11:If y = 5 cos x – 3 sin x, prove that 2 2 0
Question 12:If y = cos–1 x, Find 2 2 d y dx in terms of y alone.
Question 13:If y = 3 cos (log x) + 4 sin (log x), show that x2 y2 + xy1 + y = 0
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 =
Question 16:If ey (x + 1) = 1, show that 2 2 2 d y dy dx dx =
Question 17:If y = (tan–1 x)2, show that (x2 + 1)2 y2 + 2x (x2 + 1) y1 = 2
