Exercise 5.7

x2 + 3x + 2 2. x 20 3. x . cos x

log x 5. x3 log x 6. ex sin 5x 7. e6x cos 3x 8. tan-1 x 9. log (log x) 10. sin (log x) 11. If y = 5 cos x - 3 sin x, prove that 2 0d y y dx + = MATHEMATICS140 12. If y = cos-1 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 + B enx, show that 2 ( ) 0d y dy m n mnydxdx − + + = 15. If y = 500e7x + 600e-7x, show that 2 49d y y dx = 16. If ey (x + 1) = 1, show that 22/2 d y dy dxdx  =    17. If y = (tan-1 x)2, show that ( x2 + 1) 2 y2 + 2x (x2 + 1) y 1 = 2