[r]
(1)5/> y:= (1/3*(cos(x)^4)(sin(x))^4); y := cos( x ) sin( x ) 1/> y:= 2*sin(x)+cos(2*x); y := sin( x ) cos( x ) > y1:=diff(y,x); y1 := cos( x ) sin( x ) sin( x ) cos( x ) > y1:=diff(y,x); y1 := cos( x ) sin( x ) > y2:=solve(y1=0,{x}); 1 y2 := { x }, { x }, { x }, { x } 2 6 > y2:=solve(y1=0,{x}); 1 { x }, { x }, { x } 2 2/> y:= (1/3*(sin(x)^3)-(cos(x))^2); y := sin( x ) cos( x ) 6/ > y:= (cos(x)^4)-(sin(x))^4; y := cos( x ) sin( x ) > y1:=diff(y,x); y1 := 4 cos( x ) sin( x ) sin( x ) cos( x ) > y1:=diff(y,x); y1 := sin( x ) cos( x ) cos( x ) sin( x ) > y2:=solve(y1=0,{x}); 1 y2 := { x }, { x }, { x } 2 > y2:=solve(y1=0,{x}); 1 { x } { x }, { x } 2 7/ > y:= (cos(x)^6)+(sin(x))^6; y := cos( x ) sin( x ) 3/ > y:= (1/3*(cos(x)^3)+(sin(x))^2); y := cos( x ) sin( x ) > y1:=diff(y,x); y1 := 6 cos( x ) sin( x ) sin( x ) cos( x ) > y1:=diff(y,x); y1 := cos( x ) sin( x ) cos( x ) sin( x ) > y2:=solve(y1=0,{x}); 1 { x }, { x }, { x } 2 > y2:=solve(y1=0,{x}); 1 { x }, { x }, { x } 2 {x 4/ > y:= 1 }, { x } 4 8/ > y:= 3*sin(x)+sin(3*x); y := sin( x ) sin( x ) (1/3*(cos(x)^4)+(sin(x))^4); y := cos( x ) sin( x ) > y1:=diff(y,x); y1 := cos( x ) cos( x ) > y1:=diff(y,x); y1 := cos( x ) sin( x ) sin( x ) cos( x ) > y2:=solve(y1=0,{x}); 1 y2 := { x }, { x }, { x } 4 > y2:=solve(y1=0,{x}); 1 { x }, { x }, { x } 2 9/ {x 1 }, { x } 6 > y:= 3*sin(x)-sin(3*x); y := sin( x ) sin( x ) > y1:=diff(y,x); y1 := cos( x ) cos( x ) > y2:=solve(y1=0,{x}); y2 := { x }, { x }, { x } Lop12.net (2) 10/ > y:= sin(2*x)/(2+cos(2*x)); y := 13/ sin( x ) cos( x ) > y:=(sin(x))^2 + 3*cos(2*x); y := sin( x ) cos( x ) > y1:=diff(y,x); y1 := sin( x ) cos( x ) sin( x ) > y1:=diff(y,x); cos( x ) sin( x ) y1 := cos( x ) ( cos( x ) ) > y2:=simplify(y1); y2 := 10 sin( x ) cos( x ) > y2:=simplify(y1); cos( x ) y2 := cos( x ) cos( x ) > y3:=solve(y2=0,{x}); y3 := { x }, { x } > y3:=solve(y2=0,{x}); y3 := { x } 14/ 11/ y := e x sin( x ) > y1:=diff(y,x); y1 := e x ln( e ) sin( x ) e x cos( x ) > y:= cos(2*x)/(2+sin(2*x)); y := > y:=e^(x)*sin(x); cos( x ) sin( x ) > y2:=simplify(y1); y2 := e x ( ln( e ) sin( x ) cos( x ) ) > y1:=diff(y,x); sin( x ) cos( x ) y1 := 2 sin( x ) ( sin( x ) ) > y3:=solve(y2=0,{x}); y3 := { x arctan } ln ( e) > y2:=simplify(y1); sin( x ) y2 := 5 sin( x ) cos( x ) 15/ > y3:=solve(y2=0,{x}); y3 := { x }, { x } 12 12 > y:=e^(x)*cos(x); y := e x cos( x ) > y1:=diff(y,x); y1 := e x ln( e ) cos( x ) e x sin( x ) > y2:=simplify(y1); y2 := e x ( ln( e ) cos( x ) sin( x ) ) > y:=sqrt( 12/ cos(1*x))+sqrt(sin(x)); y := cos( x ) sin( x ) > y3:=solve(y2=0,{x}); y3 := { x arctan ( ln( e ) ) } > y1:=diff(y,x); cos( x ) sin( x ) y1 := cos( x ) sin( x ) 16/ > y:=e^(x)*(x-1); y := e x ( x ) > y1:=diff(y,x); y1 := e x ln( e ) ( x ) e x > y2:=simplify(y1); ( 3/2 ) ( 3/2 ) sin( x ) cos( x ) y2 := cos( x ) sin( x ) > y2:=simplify(y1); y2 := e x ln( e ) x e x ln( e ) e x > y3:=solve(y2=0,{x}); y3 := { x }, { x } 4 > y3:=solve(y2=0,{x}); ln( e ) y3 := { x } ln( e ) Lop12.net (3) 17/ > y:=(x)*e^(1-x); y := x e (1 x ) > y1:=diff(y,x); y1 := x e x x e x ln( e ) > y2:=simplify(y1); (1 x ) (1 x ) y2 := e xe ln( e ) > y2:=solve(y1=0,{x}); > y3:=solve(y2=0,{x}); y3 := { x } ln( e ) y2 := { x }, { x 2 (x 1) > y1:=diff(y,x); (x 1) (x 1) y1 := x e x2 e ln( e ) > y1:=diff(y,x); (x 1) (x 1) y1 := e xe ln( e ) > y2:=solve(y1=0,{x}); y2 := { x }, { x 2 > y2:=simplify(y1); (x 1) (x 1) y2 := e xe ln( e ) y := x e > y1:=diff(y,x); y1 := e > y:=(x)^2*e^(x^2); y := x e (x ) > y1:=diff(y,x); y1 := x e (x ) x3 e > y2:=simplify(y1); y2 := x e (x ) x3 e (x ) (x ) y1 := x e ln( e ) > y1:=diff(y,x); 1 y1 := 4x } ln( e ) (x 1) 4x > y2:=solve(y1=0,{x}); y2 := { x } 25 / > y:=(sqrt(4+x^2))-(sqrt(x^2)); y := x x > y1:=diff(y,x); 2x e x) ln( e ) (x 1) ( xe 24/ > y:=(sqrt(4+x))+(sqrt(4-x)); y := x x > y1:=diff(y,x); (x 1) ln( e ) > y:=(x)^2*e^(x^2-1); y := x e ( x) ( x) > y2:=solve(y1=0,{x}); y2 := { x } ln( e ) > y3:=solve(y2=0,{x}); y3 := { x }, { x }, { x ln( e ) 20/ } ln( e ) 23/ > y:=(x)*e^(sqrt(x)); > y3:=solve(y2=0,{x}); y3 := { x } ln( e ) 19/ } ln( e ) 22/ > y:=(x)^2*e^(x-1); (x 1) y := x e > y:=(x)*e^(x-1); y := x e } ln( e ) 21/ > y:=(x)^2*e^(x); y := x e x > y1:=diff(y,x); (1 x ) (1 x ) y1 := e xe ln( e ) 18/ }, { x ln( e ) y2 := { x }, { x y1 := ln( e ) > y2:=solve(y1=0,{x}); x 4x > y2:=solve(y1 =0,{x}); x=0 Lop12.net x x2 (4) 26/ > y:=(sqrt(4-x^2))+(sqrt(x^2)); y := x x > y2:=solve(y1 =0,{x}); y2 := { x } > y1:=diff(y,x); 31/ > y:= 3*sqrt(9-x)+6*sqrt(x+6); y := x x y1 := x x2 x x2 > y1:=diff(y,x); y1 := 9x > y2:=solve(y1 =0,{x}); y2 := { x }, { x } > y2:=solve(y1 =0,{x}); y2 := { x } x=0 > restart: 27/ > y:= x+(sqrt(2-x^2)); y := x x > y1:=diff(y,x); y1 := 32/ > y:= 3*sqrt(12-x)+6*sqrt(x+8); y := 12 x x > y1:=diff(y,x); y1 := 12 x x x2 33/ > y:= x*ln(x); y := x ln( x ) > y:= 3*x-5*(sqrt(4+x^2)); > y1:=diff(y,x); y1 := ln( x ) y := x x > y1:=diff(y,x); y1 := > y2:=solve(y1 =0,{x}); ( -1 ) y2 := { x e } 5x x2 34/ > y:= ln(x)/x; > y2:=solve(y1 =0,{x}); y2 := { x } y := > y1:=diff(y,x); 29/> y:= 6*x-8*(sqrt(4*x-x^2)); y := x x x > y1:=diff(y,x); y1 := y1 := x x2 ln( x ) x2 x2 35/ > y:= ln(x)/x^2; ln( x ) y := x2 > y1:=diff(y,x); > y:= 3*sqrt(4-x)+6*sqrt(x+6); y1 := y := x x > y1:=diff(y,x); y1 := 4x ln( x ) x > y2:=solve(y1 =0,{x}); y2 := { x e } (4 x) > y2:=solve(y1 =0,{x}); y2 := { x } 30/ x8 > y2:=solve(y1 =0,{x}); y2 := { x } > y2:=solve(y1 =0,{x}); y2 := { x } 28/ x6 ln( x ) x3 x3 > y2:=solve(y1 =0,{x}); ( 1/2 ) y2 := { x e } x6 Lop12.net (5) 36/ > y:= ln(x)*x^2; y := ln( x ) x 41/ > y:=1*x-1*ln(5*x^2-10*x+10); y := x ln( x 10 x 10 ) > y1:=diff(y,x); y1 := x x ln( x ) > y1:=diff(y,x); > y2:=solve(y1 =0,{x}); ( -1 /2 ) y2 := { x e } y1 := 10 x 10 x 10 x 10 37/ > y:=( x^2)*ln(x^2); y := x ln( x ) > y2:=solve(y1=0,{x}); y2 := { x }, { x } > y1:=diff(y,x); y1 := x ln( x ) x 42/ > y:=1*x-1*ln(1*x^2-10*x+10); y := x ln( x 10 x 10 ) > y2:=solve(y1 =0,{x}); y2 := { x e ( -1 ) }, { x e ( -1 ) > y1:=diff(y,x); } y1 := 38/ > y:=1*x-ln(x^2-1*x+1); y := x ln( x x ) > y2:=solve(y1=0,{x}); y2 := { x 10 }, { x } > y1:=diff(y,x); 43/ > y:=1*x*e^(-x^2/2); 2x1 y1 := x x1 y := x e > y2:=solve(y1=0,{x}); y2 := { x }, { x } y1 := y1 := e ( 10 x ) x x 10 x2 e ( 1/2 x ) ln( e ) } ln( e ) 44/ > y:=tan(x)+cot(x); y := tan ( x ) cot ( x ) > y1:=diff(y,x); y1 := tan ( x ) cot ( x ) 40/ > y:=1*x+2*ln(5*x^2+5*x+10); y := x ln( x x 10 ) y1 := ( 1/2 x ) > y2:=solve(y1=0,{x}); y2 := { x }, { x ln( e ) > y2:=solve(y1=0,{x}); y2 := { x }, { x } > y1:=diff(y,x); ( 1/2 x ) > y1:=diff(y,x); 39/ > y:=1*x-2*ln(5*x^2+5*x+10); y := x ln( x x 10 ) > y1:=diff(y,x); x 10 x 10 x 10 > y2:=solve(y1=0,{x}); 1 y2 := { x }, { x } 4 ( 10 x ) x x 10 > y2:=solve(y1=0,{x}); y2 := { x -1 }, { x -4 } Lop12.net (6)