用Maple求参数方程的导数

 

x:=t->2*t^2;
       y:=t->sin(t);

Dx:=diff(x(t),t);

Dy:=diff(y(t),t);

DyDx=Dy/Dx;

 

x:=t->exp(t)*sin(t);
       y:=t->exp(t)*cos(t);

Dx:=D(x)(t);

Dy:=D(y)(t);

DyDx=Dy/Dx;

simplify(%);

 

  或

x:=t->exp(t)*sin(t);

y:=t->exp(t)*cos(t);

a:=Pi/3:

Dx:=D(x)(a);

Dy:=D(y)(a);

DyDx=Dy/Dx;

simplify(%);

 

 

参数方程的高阶导数

 

 

  

x:=t->2*t^2;y:=t->sin(t);

Y:=D(y)(t)/D(x)(t);

Yi:=t->D(y)(t)/D(x)(t);

Er:=D(Yi)(t)/D(x)(t);

simplify(%);

  

   

 

（用微分记号D）  

x:=t->2*t^2;

y:=t->sin(t);

(D(x)(t)*(D@@2)(y)(t)-D(y)(t)*(D@@2)(x)(t))/(D(x)(t))^3;

simplify(%);

 

  （或用记号diff）

x:=t->2*t^2;

y:=t->sin(t);

(diff(x(t),t)*diff(y(t),t$2)-diff(x(t),t$2)*diff(y(t),t))/diff(x(t),t)^3;

simplify(%);

 

  

       x:=t->2*t^2:y:=t->sin(t):

Yi:=D(y)(t)/D(x)(t);

Yi:=t->D(y)(t)/D(x)(t):

Er:=D(Yi)(t)/D(x)(t);

Er:=simplify(%);

Er:=t->D(Yi)(t)/D(x)(t):

San:=D(Er)(t)/D(x)(t);

San:=simplify(%);

 

 

只显示最终结果：

x:=t->2*t^2:y:=t->sin(t):

Yi:=D(y)(t)/D(x)(t);

Yi:=t->D(y)(t)/D(x)(t):

Er:=D(Yi)(t)/D(x)(t):

Er:=simplify(%);

Er:=t->D(Yi)(t)/D(x)(t):

San:=D(Er)(t)/D(x)(t):

San:=simplify(%);