# LaTeX2HTML 2022 (Released January 1, 2022)
# Associate images original text with physical files.
$key = q//;
$cached_env_img{$key} = q|<IMG
  STYLE="height: 2.38ex; vertical-align: 176.13ex; " SRC="|."$dir".q|img27.png"
 ALT="\begin{maple}
&gt; f := proc(x,b,n) local i,s;
&gt;  ...">|; 
$key = q/{maple}><sin(x)+cos(x)^2|x>;2<sin(x)+cos(x)|x>{par{{maple};AAT/;
$cached_env_img{$key} = q|<IMG
  STYLE="height: 2.38ex; vertical-align: 176.27ex; " SRC="|."$dir".q|img15.png"
 ALT="\begin{maple}
&gt; &lt;sin(x)+cos(x)^2\vert x&gt;;
&lt;sin(x) + cos(x) \vert x&gt;
\end{maple}">|; 
$key = q/{maple}>D(G);x->cos(x)-2cos(x)sin(x){par{{maple};AAT/;
$cached_env_img{$key} = q|<IMG
  STYLE="height: 2.38ex; vertical-align: 176.27ex; " SRC="|."$dir".q|img20.png"
 ALT="\begin{maple}
&gt; D(G);
x -&gt; cos(x) - 2 cos(x) sin(x)
\end{maple}">|; 
$key = q/{maple}>D(y)=solve(",D(y));23-yD(x)-2yD(x)x-3D(x)D(y)=--------------------------------222yx+3yx+1{par{{maple};AAT/;
$cached_env_img{$key} = q|<IMG
  STYLE="height: 2.38ex; vertical-align: 176.27ex; " SRC="|."$dir".q|img11.png"
 ALT="\begin{maple}
&gt; D(y) = solve('',D(y));
- y D(x) - 2 y D(x) x - 3 D(x)
D(y) = &mdash;&mdash;&mdash;&mdash;&mdash;&mdash;&mdash;&mdash;&mdash;&mdash;&ndash;
2 y x + 3 y x + 1
\end{maple}">|; 
$key = q/{maple}>F:=sin+cos^2;2F:=sin+cos{maple};AAT/;
$cached_env_img{$key} = q|<IMG
  STYLE="height: 196.25ex; vertical-align: -0.57ex; " SRC="|."$dir".q|img1.png"
 ALT="\begin{maple}
&gt; F := sin+cos^2;
F := sin + cos
\end{maple}">|; 
$key = q/{maple}>F:=sin+cos^2;2F:=sin+cos{par{>F(x);2sin(x)+cos(x){par{>diff(F(x),x)-D(F)(x);{par{0{par{{maple};AAT/;
$cached_env_img{$key} = q|<IMG
  STYLE="height: 2.38ex; vertical-align: 176.27ex; " SRC="|."$dir".q|img13.png"
 ALT="\begin{maple}
&gt; F := sin+cos^2;
F := sin + cos
&gt; F(x);
sin(x) + cos(x)
&gt; diff(F(x),x) - D(F)(x);
\end{maple}">|; 
$key = q/{maple}>G:=unapply(F(x),x);2G:=x->sin(x)+cos(x){maple};AAT/;
$cached_env_img{$key} = q|<IMG
  STYLE="height: 2.59ex; vertical-align: 176.13ex; " SRC="|."$dir".q|img14.png"
 ALT="\begin{maple}
&gt; G := unapply(F(x),x);
G := x -&gt; sin(x) + cos(x)
\end{maple}">|; 
$key = q/{maple}>diff(f(x),x)-g(x);0{maple};AAT/;
$cached_env_img{$key} = q|<IMG
  STYLE="height: 2.59ex; vertical-align: 176.13ex; " SRC="|."$dir".q|img25.png"
 ALT="\begin{maple}
&gt; diff(f(x),x) - g(x);
\end{maple}">|; 
$key = q/{maple}>diff(f(x),x);d----f(x)dx{par{>convert(",D);D(f)(x){par{>unapply(",x);D(f){par{{maple};AAT/;
$cached_env_img{$key} = q|<IMG
  STYLE="height: 2.38ex; vertical-align: 176.27ex; " SRC="|."$dir".q|img21.png"
 ALT="\begin{maple}
&gt; diff(f(x),x);
&mdash;- f(x)
&gt; convert('',D);
D(f)(x)
&gt; unapply('',x);
\end{maple}">|; 
$key = q/{maple}>diff(f(x^2),x);22xD(f)(x){par{>diff(f(x^2,x*y),x);222xD[1](f)(x,xy)+yD[2](f)(x,xy){par{>D(f@g);{par{D(f)@gD(g){par{{maple};AAT/;
$cached_env_img{$key} = q|<IMG
  STYLE="height: 2.38ex; vertical-align: 176.27ex; " SRC="|."$dir".q|img8.png"
 ALT="\begin{maple}
&gt; diff(f(x^2),x);
2 x D(f)(x )
&gt; diff(f(x^2,x*y),x);
2 2...
...)(x , x y) + y D[2](f)(x , x y)
&gt; D(f@g);
D(f)@g D(g)
\end{maple}">|; 
$key = q/{maple}>diff(sin(cos(x)),x);-cos(cos(x))sin(x){par{>D(sin@cos);(2)-cossin{maple};AAT/;
$cached_env_img{$key} = q|<IMG
  STYLE="height: 2.59ex; vertical-align: 176.13ex; " SRC="|."$dir".q|img4.png"
 ALT="\begin{maple}
&gt; diff( sin(cos(x)), x );
- cos(cos(x)) sin(x)
&gt; D( sin@cos );
- cos sin
\end{maple}">|; 
$key = q/{maple}>diff(sin(x)^2,x);2sin(x)cos(x){par{>D(sin^2);2cossin{maple};AAT/;
$cached_env_img{$key} = q|<IMG
  STYLE="height: 2.38ex; vertical-align: 176.27ex; " SRC="|."$dir".q|img3.png"
 ALT="\begin{maple}
&gt; diff( sin(x)^2, x );
2 sin(x) cos(x)
&gt; D(sin^2);
2 cos sin
\end{maple}">|; 
$key = q/{maple}>eq:=y^2*x+y^3*x^2+y+3*x=0;{par{232eq:=yx+yx+y+3x=0{par{{maple};AAT/;
$cached_env_img{$key} = q|<IMG
  STYLE="height: 2.59ex; vertical-align: 176.26ex; " SRC="|."$dir".q|img9.png"
 ALT="\begin{maple}
&gt; eq := y^2*x + y^3*x^2 + y + 3*x = 0;
2 3 2
eq := y x + y x + y + 3 x = 0
\end{maple}">|; 
$key = q/{maple}>expand(F-eval(G));{par{0{maple};AAT/;
$cached_env_img{$key} = q|<IMG
  STYLE="height: 2.38ex; vertical-align: 176.27ex; " SRC="|."$dir".q|img19.png"
 ALT="\begin{maple}
&gt; expand(F-eval(G));
\end{maple}">|; 
$key = q/{maple}>expand(eval(G));2sin+cos{par{{maple};AAT/;
$cached_env_img{$key} = q|<IMG
  STYLE="height: 2.38ex; vertical-align: 176.27ex; " SRC="|."$dir".q|img18.png"
 ALT="\begin{maple}
&gt; expand(eval(G));
sin + cos
\end{maple}">|; 
$key = q/{maple}>expand(f1-f2);0{par{{maple};AAT/;
$cached_env_img{$key} = q|<IMG
  STYLE="height: 2.59ex; vertical-align: 176.13ex; " SRC="|."$dir".q|img17.png"
 ALT="\begin{maple}
&gt; expand(f1-f2);
\end{maple}">|; 
$key = q/{maple}>f(x);22sin(x)x+2x{par{>diff(",x);2cos(x)x+2sin(x)x+4x{par{{maple};AAT/;
$cached_env_img{$key} = q|<IMG
  STYLE="height: 2.59ex; vertical-align: 176.13ex; " SRC="|."$dir".q|img23.png"
 ALT="\begin{maple}
&gt; f(x);
sin(x) x + 2 x
&gt; diff('',x);
cos(x) x + 2 sin(x) x + 4 x
\end{maple}">|; 
$key = q/{maple}>f1:=sin(x)+cos(x)^2:>f2:=sin(x)+cos(2*x)slash2+1slash2:{maple};AAT/;
$cached_env_img{$key} = q|<IMG
  STYLE="height: 2.59ex; vertical-align: 176.13ex; " SRC="|."$dir".q|img16.png"
 ALT="\begin{maple}
&gt; f1 := sin(x)+cos(x)^2:
&gt; f2 := sin(x)+cos(2*x)/2+1/2:
\end{maple}">|; 
$key = q/{maple}>g:=PD(f,1);g:=proc(x)localt,s,sx,tx;sx:=cos(x);s:=sin(x);tx:=2*x;t:=x^2;sx*t+s*tx+2*txend{maple};AAT/;
$cached_env_img{$key} = q|<IMG
  STYLE="height: 2.38ex; vertical-align: 176.27ex; " SRC="|."$dir".q|img24.png"
 ALT="\begin{maple}
&gt; g := PD(f,1);
g := proc(x)
local t,s,sx,tx;
sx := cos(x); s := sin(x); tx := 2*x; t := x^2; sx*t+s*tx+2*tx
\end{maple}">|; 
$key = q/{maple}>map(D,eq);22232D(y)yx+yD(x)+3D(y)yx+2yD(x)x+D(y)+3D(x)=0{par{{maple};AAT/;
$cached_env_img{$key} = q|<IMG
  STYLE="height: 2.45ex; vertical-align: 176.27ex; " SRC="|."$dir".q|img10.png"
 ALT="\begin{maple}
&gt; map(D,eq);
2 2 2 3
2 D(y) y x + y D(x) + 3 D(y) y x + 2 y D(x) x + D(y) + 3 D(x) = 0
\end{maple}">|; 
$key = q/{maple}>read`PD.m`:>f:=proc(x)locals,t;s:=sin(x);t:=x^2;s*t+2*tend:{maple};AAT/;
$cached_env_img{$key} = q|<IMG
  STYLE="height: 2.38ex; vertical-align: 176.27ex; " SRC="|."$dir".q|img22.png"
 ALT="\begin{maple}
&gt; read \lq PD.m\lq :
&gt; f := proc(x) local s,t; s := sin(x); t := x^2; s*t+2*t end:
\end{maple}">|; 
$key = q/{maple}>subs(D(x)=1,");23-y-2yx-3D(y)=-------------------222yx+3yx+1{par{{maple};AAT/;
$cached_env_img{$key} = q|<IMG
  STYLE="height: 2.38ex; vertical-align: 176.27ex; " SRC="|."$dir".q|img12.png"
 ALT="\begin{maple}
&gt; subs(D(x)=1,'');
- y - 2 y x - 3
D(y) = &mdash;&mdash;&mdash;&mdash;&mdash;&mdash;-
2 y x + 3 y x + 1
\end{maple}">|; 
$key = q/{maple}>taylor(f(x),x);{par{(2)2(3)3(4)4f(0)+D(f)(0)x+1slash2D(f)(0)x+1slash6D(f)(0)x+1slash24D(f)(0)x{par{(5)56+1slash120D(f)(0)x+O(x){par{{maple};AAT/;
$cached_env_img{$key} = q|<IMG
  STYLE="height: 2.38ex; vertical-align: 176.27ex; " SRC="|."$dir".q|img6.png"
 ALT="\begin{maple}
&gt; taylor(f(x),x);
(2) 2 (3) 3 (4) 4
f(0) + D(f)(0) x + 1/2 D...
...0) x + 1/24 D (f)(0) x
(5) 5 6
+ 1/120 D (f)(0) x + O(x )
\end{maple}">|; 
$key = q/{maple}{par{>F(1.0);1.133397567{par{>F(Pislash3);1slash21slash23+1slash4{par{>F(x);2sin(x)+cos(x){par{{maple};AAT/;
$cached_env_img{$key} = q|<IMG
  STYLE="height: 2.45ex; vertical-align: 176.27ex; " SRC="|."$dir".q|img2.png"
 ALT="\begin{maple}
&gt; F(1.0);
1.133397567
&gt; F(Pi/3);
1/2 3 + 1/4
&gt; F(x);
sin(x) + cos(x)
\end{maple}">|;