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> f:=2*x^3+5*x*y+2*y^2;
 

2*x^3+5*x*y+2*y^2 

> fx:=diff(f,x);
 

6*x^2+5*y 

> fy:=diff(f,y);
 

5*x+4*y 

> subs({x=1,y=-2},fx);
 

-4 

> subs({x=1,y=-2},fy);
 

-3 

> f:=exp(x-y)*sin(2*x^2-3*x*y+4*y);
 

exp(x-y)*sin(2*x^2-3*x*y+4*y) 

> fx:=diff(f,x);
 

exp(x-y)*sin(2*x^2-3*x*y+4*y)+exp(x-y)*cos(2*x^2-3*x*y+4*y)*(4*x-3*y)
exp(x-y)*sin(2*x^2-3*x*y+4*y)+exp(x-y)*cos(2*x^2-3*x*y+4*y)*(4*x-3*y) 

> fx:=simplify(fx);
 

exp(x-y)*(sin(2*x^2-3*x*y+4*y)+4*cos(2*x^2-3*x*y+4*y)*x-3*cos(2*x^2-3*x*y+4*y)*y)
exp(x-y)*(sin(2*x^2-3*x*y+4*y)+4*cos(2*x^2-3*x*y+4*y)*x-3*cos(2*x^2-3*x*y+4*y)*y) 

> fy:=diff(f,y);
 

-exp(x-y)*sin(2*x^2-3*x*y+4*y)+exp(x-y)*cos(2*x^2-3*x*y+4*y)*(-3*x+4)
-exp(x-y)*sin(2*x^2-3*x*y+4*y)+exp(x-y)*cos(2*x^2-3*x*y+4*y)*(-3*x+4) 

> fy:=simplify(fy);
 

-exp(x-y)*(sin(2*x^2-3*x*y+4*y)+3*cos(2*x^2-3*x*y+4*y)*x-4*cos(2*x^2-3*x*y+4*y))
-exp(x-y)*(sin(2*x^2-3*x*y+4*y)+3*cos(2*x^2-3*x*y+4*y)*x-4*cos(2*x^2-3*x*y+4*y)) 

> f:=2*x^3+5*x*y+2*y^2;
 

2*x^3+5*x*y+2*y^2 

> fx:=diff(f,x);
 

6*x^2+5*y 

> fy:=diff(f,y);
 

5*x+4*y 

> fxx:=diff(f,x,x);
 

12*x 

> fxy:=diff(f,x,y);
 

5 

> fyx:=diff(f,y,x);
 

5 

> fyy:=diff(f,y,y);
 

4 

> fxxx:=diff(f,x,x,x);
 

12 

> fxxy:=diff(f,x,x,y);
 

0 

> fxyy:=diff(f,x,y,y);
 

0 

> fyyy:=diff(f,y,y,y);
 

0 

> f:=exp(x^2+x*y);
 

exp(x^2+x*y) 

> fx:=diff(f,x);
 

(2*x+y)*exp(x^2+x*y) 

> fy:=diff(f,y);
 

x*exp(x^2+x*y) 

> fxx:=simplify(diff(f,x,x));
 

exp(x*(x+y))*(2+4*x^2+4*x*y+y^2) 

> fxy:=simplify(diff(f,x,y));
 

exp(x*(x+y))*(1+2*x^2+x*y) 

> fyy:=simplify(diff(f,y,y));
 

x^2*exp(x*(x+y)) 

> fxxx:=simplify(diff(f,x,x,x));
 

exp(x*(x+y))*(12*x+6*y+8*x^3+12*x^2*y+6*x*y^2+y^3) 

> fxxy:=simplify(diff(f,x,x,y));
 

exp(x*(x+y))*(6*x+2*y+4*x^3+4*x^2*y+x*y^2) 

> fxyy:=simplify(diff(f,x,y,y));
 

x*exp(x*(x+y))*(2+2*x^2+x*y) 

> fyyy:=simplify(diff(f,y,y,y));
 

x^3*exp(x*(x+y)) 

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