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Apr 6th, 2020
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  1.  
  2.  
  3. \noindent
  4. %%%%%%%%%%%%%%%
  5. %%% INPUT:
  6. \begin{minipage}[t]{4em}\color{red}\bf
  7. (\% i35)
  8. \end{minipage}
  9. \begin{minipage}[t]{\textwidth}\color{blue}
  10. 'diff(y, x) = (y*(x*cos(x)-y-sin(x)))/(x\^{}2 + y*x);
  11.  
  12.  
  13. \end{minipage}
  14. %%% OUTPUT:
  15. \[\displaystyle \tag{\% o35}
  16. \frac{d}{d x} y=\frac{\left( -y-\sin{(x)}+x \cos{(x)}\right)  y}{x y+{{x}^{2}}}\mbox{}
  17. \]
  18. %%%%%%%%%%%%%%%
  19.  
  20. \noindent
  21. %%%%%%%%%%%%%%%
  22. %%% INPUT:
  23. \begin{minipage}[t]{4em}\color{red}\bf
  24. (\% i27)
  25. \end{minipage}
  26. \begin{minipage}[t]{\textwidth}\color{blue}
  27. f0(x, y):= y = sin(x)-x*log(y);
  28.  
  29.  
  30. \end{minipage}
  31. %%% OUTPUT:
  32. \[\displaystyle \tag{\% o27}
  33. \operatorname{f0}\left( x,y\right) :=y=\sin{(x)}-x \log{(y)}\mbox{}
  34. \]
  35. %%%%%%%%%%%%%%%
  36.  
  37. \noindent
  38. %%%%%%%%%%%%%%%
  39. %%% INPUT:
  40. \begin{minipage}[t]{4em}\color{red}\bf
  41. (\% i28)
  42. \end{minipage}
  43. \begin{minipage}[t]{\textwidth}\color{blue}
  44. f0(pi/2, 1);
  45.  
  46.  
  47. \end{minipage}
  48. %%% OUTPUT:
  49. \[\displaystyle \tag{\% o28}
  50. 1=\sin{\left( \frac{pi}{2}\right) }\mbox{}
  51. \]
  52. %%%%%%%%%%%%%%%
  53.  
  54. \noindent
  55. %%%%%%%%%%%%%%%
  56. %%% INPUT:
  57. \begin{minipage}[t]{4em}\color{red}\bf
  58. (\% i40)
  59. \end{minipage}
  60. \begin{minipage}[t]{\textwidth}\color{blue}
  61. d: diff(f0(x, y));
  62.  
  63.  
  64. \end{minipage}
  65. %%% OUTPUT:
  66. \[\displaystyle \tag{d}
  67. \operatorname{del}(y)=\left( \cos{(x)}-\log{(y)}\right)  \operatorname{del}(x)-\frac{x \operatorname{del}(y)}{y}\mbox{}
  68. \]
  69. %%%%%%%%%%%%%%%
  70.  
  71. \noindent
  72. %%%%%%%%%%%%%%%
  73. %%% INPUT:
  74. \begin{minipage}[t]{4em}\color{red}\bf
  75. (\% i43)
  76. \end{minipage}
  77. \begin{minipage}[t]{\textwidth}\color{blue}
  78. solve(d, del(y))/del(x);
  79.  
  80.  
  81. \end{minipage}
  82. %%% OUTPUT:
  83. \[\displaystyle \tag{\% o43}
  84. [\frac{\operatorname{del}(y)}{\operatorname{del}(x)}=-\frac{y \log{(y)}-\cos{(x)} y}{y+x}]\mbox{}
  85. \]
  86. %%%%%%%%%%%%%%%
  87.  
  88. \noindent
  89. %%%%%%%%%%%%%%%
  90. %%% INPUT:
  91. \begin{minipage}[t]{4em}\color{red}\bf
  92. (\% i31)
  93. \end{minipage}
  94. \begin{minipage}[t]{\textwidth}\color{blue}
  95. f(yp):= yp = (y*(x*cos(x)-y-sin(x)))/(x\^{}2 + y*x);
  96.  
  97.  
  98. \end{minipage}
  99. %%% OUTPUT:
  100. \[\displaystyle \tag{\% o31}
  101. \operatorname{f}\left( \mathit{yp}\right) :=\mathit{yp}=\frac{y\, \left( x \cos{(x)}-y-\sin{(x)}\right) }{{{x}^{2}}+y x}\mbox{}
  102. \]
  103. %%%%%%%%%%%%%%%
  104.  
  105. \noindent
  106. %%%%%%%%%%%%%%%
  107. %%% INPUT:
  108. \begin{minipage}[t]{4em}\color{red}\bf
  109. (\% i32)
  110. \end{minipage}
  111. \begin{minipage}[t]{\textwidth}\color{blue}
  112. f(-(y*log(y)-cos(x)*y)/(y+x));
  113.  
  114.  
  115. \end{minipage}
  116. %%% OUTPUT:
  117. \[\displaystyle \tag{\% o32}
  118. \frac{\cos{(x)} y-y \log{(y)}}{y+x}=\frac{\left( -y-\sin{(x)}+x \cos{(x)}\right)  y}{x y+{{x}^{2}}}\mbox{}
  119. \]
  120. %%%%%%%%%%%%%%%
  121.  
  122. \noindent
  123. %%%%%%%%%%%%%%%
  124. %%% INPUT:
  125. \begin{minipage}[t]{4em}\color{red}\bf
  126. (\% i33)
  127. \end{minipage}
  128. \begin{minipage}[t]{\textwidth}\color{blue}
  129. log(y)=y+sin(x);
  130.  
  131.  
  132. \end{minipage}
  133. %%% OUTPUT:
  134. \[\displaystyle \tag{\% o33}
  135. \log{(y)}=y+\sin{(x)}\mbox{}
  136. \]
  137. %%%%%%%%%%%%%%%
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