REVIEW OF DIFFERENTIATION Rules 1.Constant: dc=0 2.Constant Multiple: f()=cf(x) d 3.Sum: f(田±gxl=f'e±gx 4.Product: d dx fxg)=f(g)+gefe 5.Quotient: dfx-gx)f"x)-fx)g'(） dx g(x) 6.Chain: [g(x2 足fgx》=fgxg'(x) 7.Power: d x”=nxn-1 8.Power: dx ng(g( dx Functions Trigonometric: 9. d d sinx=cosx 10. 11. dx dx cosx=-sinx d tanx=seex d 12.4cotx=-csc 13. d 14. dx -secx=sec xtanx cscx=-cscx cot Inverse trigonometric: 15d 1 16. d cos-1x=-- 1 17. dx 1-x2 dx V1-x2 dx 1+x2 18 ot-x=-1 -sec-1x=- 1 19. 20. d csc-1 x=-- 1 dx 1+x2 dx Ve2-1 dx Vx2-1 Hyperbolic: 21 sinhx=coshx 22. d -cosh x=sinhx 23. dx dx d tanhx=sech2x dx 24 -coth x=-csch2x 25. d sechx=-sech xtanhx 26. d -cschx =-csch x cothx dx dx dx Inverse hyperbolic: 27 -sinh-1x=- 1 28. d cosh-1x=- 1 29.d tanhx=1 dx x2+1 dx x2-1 1-x2 30. -coth=7 31. d 1-x2 sech-Ix=- d 32. csch-1x=- xv1-x2 dx Ve2+1 Exponential: mhvve 34.4b=banb) dx Logarithmic: 5县g=生 36. 1 dx d logx= d x(nb)Rules 1. Constant: d dx c = 0 2. Constant Multiple: d dx cf (x) = c f ￾(x) . Sum: d dx [f (x) ± g(x)] = ￾ f (x) ± g￾(x) 4. Product: d dx f (x)g(x) = f (x)g￾(x) + g(x) f ￾(x) 5. Quotient: d dx f (x) g(x) = g(x)f (x) ￾ f (x)g (x) [ g(x)]2 6. Chain: d dx f (g(x)) = f ￾(g(x))g￾(x) 7. Power: d dx xn = nxn￾1 8. Power: d dx [ g(x)]n = n[ g(x)]n 1 g￾(x) Functions Trigonometric: 9. d dx sin x = cos x 10. d dx cos x = ￾ sin x 11. d dx tan x = sec2 x 12. d dx cot x = ￾ csc2 x 13. d dx sec x = sec x tan x 14. d dx csc x = ￾ csc x cot x Inverse trigonometric: 15. d dx sin￾1 x = 1 1 ￾ x2 16. d dx cos￾1 x = ￾ 1 1 ￾ x2 17. d dx tan￾1 x = 1 1 + x2 18. d dx cot￾1 x = ￾ 1 1 + x2 19. d dx sec￾1 x = 1 x x2 ￾1 20. d dx csc￾1 x = ￾ 1 x x2 ￾1 Hyperbolic: 21. d dx sinh x = cosh x 22. d dx cosh x = sinh x 23. d dx tanh x = sech2 x 24. d dx coth x = ￾ csch2 x 25. d dx sech x = ￾ sech x tanh x 26. d dx csch x = ￾ csch x coth x Inverse hyperbolic: 27. d dx sinh￾1 x = 1 x2 +1 28. d dx cosh￾1 x = 1 x2 ￾1 29. d dx tanh￾1 x = 1 1 ￾ x2 30. d dx coth￾1 x = 1 1 ￾ x2 31. d dx sech￾1 x = ￾ 1 x 1 ￾ x2 32. d dx csch￾1 x = ￾ 1 x x2 +1 Exponential: 33. d dx ex = ex 34. d dx bx = bx (lnb) Logarithmic: 35. d dx ln x = 1 x 36. d dx logb x = 1 x(lnb) ￾ ￾ ￾ 3 REVIEW OF DIFFERENTIATION