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/ Monster Media 1996 #15 / Monster Media Number 15 (Monster Media)(July 1996).ISO / math / differ.zip / OUT.TXT < prev    next >
Text File  |  1996-02-11  |  4KB  |  206 lines
  1. Input expression:
  2. x^3+x^2+x+1
  3. Output expression:
  4. 3*x^2+2*x+1
  5.  
  6. Input expression:
  7. sin(cos(x))
  8. Output expression:
  9. -sin(x)*cos(cos(x))
  10.  
  11. Input expression:
  12. (x^3+2)/x
  13. Output expression:
  14. (3*x^3-(x^3+2))/x^2
  15.  
  16. Input expression:
  17. x^0.5*(x-1)
  18. Output expression:
  19. x^0.5+0.5*(x-1)/x^0.5
  20.  
  21. Input expression:
  22. (x-4)^2
  23. Output expression:
  24. 2*(x-4)
  25.  
  26. Input expression:
  27. (7*x+1)*(7*x-1)*(x-1)
  28. Output expression:
  29. (7*x+1)*(7*x-1)+(x-1)*(7*(7*x+1)+7*(7*x-1))
  30.  
  31. Input expression:
  32. 1+1/x+1/x^2+1/x^3
  33. Output expression:
  34. -(1/x^2+2/x^3+3/x^4)
  35.  
  36. Input expression:
  37. a*x^3+b*x^2+c*x+d
  38. Output expression:
  39. 3*a*x^2+2*b*x+c
  40.  
  41. Input expression:
  42. 1/sin(x)
  43. Output expression:
  44. -cos(x)/sin(x)^2
  45.  
  46. Input expression:
  47. cos(x^2+1)^2
  48. Output expression:
  49. -4*x*sin(x^2+1)*cos(x^2+1)
  50.  
  51. Input expression:
  52. 2*cos(x^2+1)^2
  53. Output expression:
  54. -8*x*sin(x^2+1)*cos(x^2+1)
  55.  
  56. Input expression:
  57. (exp(x)-exp(-x))^(-1)
  58. Output expression:
  59. -(exp(x)+exp(-x))/(exp(x)-exp(-x))^2
  60.  
  61. Input expression:
  62. ln(sin(x)/(1-cos(x)))
  63. Output expression:
  64. ((1-cos(x))*cos(x)-sin(x)^2)/(sin(x)*(1-cos(x)))
  65.  
  66. Input expression:
  67. exp(exp(x))
  68. Output expression:
  69. exp(x)*exp(exp(x))
  70.  
  71. Input expression:
  72. ln(sin(x)*cos(x))
  73. Output expression:
  74. (-sin(x)^2+cos(x)^2)/(sin(x)*cos(x))
  75.  
  76. Input expression:
  77. 1/(x^2+x+1)
  78. Output expression:
  79. -(2*x+1)/(x^2+x+1)^2
  80.  
  81. Input expression:
  82. ln(sec(x))
  83. Output expression:
  84. tan(x)
  85.  
  86. Input expression:
  87. cos(x)*sin(x)^3
  88. Output expression:
  89. 3*cos(x)^2*sin(x)^2-sin(x)^4
  90.  
  91. Input expression:
  92. x^sin(x)
  93. Output expression:
  94. (cos(x)*ln(x)+sin(x)/x)*x^sin(x)
  95.  
  96. Input expression:
  97. (2+ln((1+x)^2))/(2-ln((1-x)^2))
  98. Output expression:
  99. (2*(2-ln((1-x)^2))/(1+x)-2*(2+ln((1+x)^2))/(1-x))/(2-ln((1-x)^2))^2
  100.  
  101. Input expression:
  102. cosec(x^2)
  103. Output expression:
  104. -2*x*cosec(x^2)*cot(x^2)
  105.  
  106. Input expression:
  107. cot(x^3)
  108. Output expression:
  109. -3*x^2*cosec(x^3)^2
  110.  
  111. Input expression:
  112. cosh(x^4+x^3)
  113. Output expression:
  114. (4*x^3+3*x^2)*sinh(x^4+x^3)
  115.  
  116. Input expression:
  117. sinh(x^3-2*x)
  118. Output expression:
  119. (3*x^2-2)*cosh(x^3-2*x)
  120.  
  121. Input expression:
  122. tanh(1/x)
  123. Output expression:
  124. -1/x^2*sech(1/x)^2
  125.  
  126. Input expression:
  127. sech(1+x)
  128. Output expression:
  129. -sech(1+x)*tanh(1+x)
  130.  
  131. Input expression:
  132. cosech(x^2-x)
  133. Output expression:
  134. -cosech(x^2-x)*(2*x-1)*coth(x^2-x)
  135.  
  136. Input expression:
  137. coth(x^5+1/x)
  138. Output expression:
  139. -(5*x^4-1/x^2)*cosech(x^5+1/x)^2
  140.  
  141. Input expression:
  142. ln(cos(x))*ln(sin(x))
  143. Output expression:
  144. ln(cos(x))*cos(x)/sin(x)-ln(sin(x))*sin(x)/cos(x)
  145.  
  146. Input expression:
  147. sinh(x)^cosh(x)
  148. Output expression:
  149. (sinh(x)*ln(sinh(x))+cosh(x)^2/sinh(x))*sinh(x)^cosh(x)
  150.  
  151. Input expression:
  152. (sin(x)+cos(x))^(sinh(x)+cosh(x))
  153. Output expression:
  154. ((cosh(x)+sinh(x))*ln(sin(x)+cos(x))+(cos(x)-sin(x))*(sinh(x)+cosh(x))/(sin(x)+cos(x)))*(sin(x)+cos(x))^(sinh(x)+cosh(x))
  155.  
  156. Input expression:
  157. arcsin(x)
  158. Output expression:
  159. 1/(1-x^2)^0.5
  160.  
  161. Input expression:
  162. arcsin((1-x^2)^0.5)
  163. Output expression:
  164. -1/(1-x^2)^0.5
  165.  
  166. Input expression:
  167. arccos(x)
  168. Output expression:
  169. -1/(1-x^2)^0.5
  170.  
  171. Input expression:
  172. arctan(x)
  173. Output expression:
  174. 1/(1+x^2)
  175.  
  176. Input expression:
  177. arcsinh(x)
  178. Output expression:
  179. 1/(1+x^2)^0.5
  180.  
  181. Input expression:
  182. arccosh(x)
  183. Output expression:
  184. 1/(x^2-1)^0.5
  185.  
  186. Input expression:
  187. arctanh(x)
  188. Output expression:
  189. 1/(1-x^2)
  190.  
  191. Input expression:
  192. sin(-x^3-3*x^2+2*x-3)
  193. Output expression:
  194. (-(3*x^2+6*x)+2)*cos(-(x^3+3*x^2)+2*x-3)
  195.  
  196. Input expression:
  197. arctanh(exp(-x^3)*((-x^2-x)-1))
  198. Output expression:
  199. (-exp(-x^3)*(2*x+1)+3*(x^2+x+1)*x^2*exp(-x^3))/(1-(exp(-x^3)*(x^2+x+1))^2)
  200.  
  201. Input expression:
  202. sin(a*x+b)+cos(c*x+d)
  203. Output expression:
  204. a*cos(a*x+b)-c*sin(c*x+d)
  205.  
  206.