DERIVADAS CON MAPLE 13 (Taller de MAPLE ACATLAN)

restart:#Derivadas de funciones directasf:=x->x^3;
> Diff(f(x),x)=diff(f(x),x);#Diff es el comando para derivar.
> Diff(f(x),x$2)=diff(f(x),x$2);#Segunada derivada se agrega $2.
> Diff(f(x),x$3)=diff(f(x),x$3);#Tercera derivada se agrega $3 y asi sucesivamente.
> Diff(f(x),x$4)=diff(f(x),x$4);#Derivada de orden n.
> restart:
> f:=x->x^4-2*x+5*x+7;
> Diff(f(x),x)=diff(f(x),x);
> Diff(f(x),x$2)=diff(f(x),x$2);
> Diff(f(x),x$3)=diff(f(x),x$3);
> Diff(f(x),x$4)=diff(f(x),x$4);
> Diff(f(x),x$5)=diff(f(x),x$5);
> restart:
> f:=x->(3-x)*(2+x);
> expand(f(x));#Realiza el producto.
> factor(%);#factor: Factoriza la expresión anterior.
> Diff(%,x)=diff(%,x);
> restart:
> f:=x->3/x^2;
> Diff(f(x),x)=diff(f(x),x);
> restart:
> f:=x->sqrt(x)+1/sqrt(x);
> Diff(f(x),x)=diff(f(x),x);
> restart:
> f:=x->(x^3-1)/(x+5);
> Diff(f(x),x)=diff(f(x),x);
> factor(%);
> restart:
> f:=x->root[3](x+1)^4;#root[3]= raíz cubica.
> Diff(f(x),x)=diff(f(x),x);
> restart:
> x:=(y^2-7)^2;
> 1/Diff(x,y)=1/diff(x,y);
> restart:
> x:=root[3](5-y^2);#Para resolver raices enecimas se cambia root[n]
> 1/Diff(x,y)=1/diff(x,y);
> restart:
> f:=x->sin(a*x);
> Diff(f(x),x)=diff(f(x),x);
> restart:
> f:=x->sin(3*x^2-1);
> Diff(f(x),x)=diff(f(x),x);
> restart:
> f:=x->sin(x/2)^2:
> Diff(f(x),x)=diff(f(x),x);
> restart:
> f:=x->root[3](tan(2*x));
> Diff(f(x),x)=diff(f(x),x);
> simplify(%,'symbolic');
> restart:
> f:=x->sin(tan(x));#Funciones trigonometricas explisitas
> Diff(f(x),x)=diff(f(x),x);
> restart:
> f:=x->sec(cos(10*x)^2);
> Diff(f(x),x)=diff(f(x),x);
> restart:
> f:=x->arcsin(5*x^2);#arcsin, es la función del arco seno
> Diff(f(x),x)=diff(f(x),x);
> restart:
> f:=x->arccos(x/2);
> Diff(f(x),x)=diff(f(x),x);
> restart:
> f:=x->arccsc(2*x);
> Diff(f(x),x)=diff(f(x),x);
> simplify(%,'symbolic');
> restart:
> f:=x->arcsin(sqrt(tan(x)));
> Diff(f(x),x)=diff(f(x),x);
> restart:#Derivada de logaritmos
> f:=x->log[10](3/x);
> Diff(f(x),x)=diff(f(x),x);
> restart:
> f:=x->ln(a*x+3);
> Diff(f(x),x)=diff(f(x),x);
> restart:
> f:=x->ln(ln(x));
> Diff(f(x),x)=diff(f(x),x);
> restart:#Derivadas de exponenciales
> f:=x->10^(x^2+5*x-6);
> Diff(f(x),x)=diff(f(x),x);
> restart:
> f:=x->x^x;
> Diff(f(x),x)=diff(f(x),x);
> restart:
> f:=x->x^(2*x);
> Diff(f(x),x)=diff(f(x),x);
> factor(%);
> simplify(%,'symbolic');
> restart:
> f:=x->sqrt(ln(sec(sqrt(x))));
> Diff(f(x),x)=diff(f(x),x);
> restart:
> f:=x->exp(10^(root[3](sin(x))));
> Diff(f(x),x)=diff(f(x),x);
> restart:
> f:=x->(sec(x)*tan(x)^3)^cos(x);
> Diff(f(x),x)=diff(f(x),x);
> factor(%);
> restart:#Derivada de una función de funciones
> F:=u->u^3;G:=u->(2*x+1)/4;
> Diff('F(G(x))',x)=diff(F(G(u)),x);
> simplify(%);
> restart:
> f:=x->x^2-8*x-3;
> g:=x->x^2+1;
> diff((f@g)(x),x);
> expand(%);
> restart:#derivadas de funciones paramétricas
> f:=a*cos(theta)=x;
> g:=b*sin(theta)=y;
> dy/dx=implicitdiff({f,g},{y,theta},y,x);
> subs(-b*cos(thetha)/a*sin(theta)=-b/a*tan(theta),%);
> #Obteniendo la segunda derivada
> 'd^2*y/dx^2'=implicitdiff({f,g},{y,theta},y,x$2);
> 'd^2*y/dx^2'=simplify(-b*(sin(theta)^2+cos(theta)^2)/a^2/sin(theta)^3,'symbolic');
> subs(-b/a^2/sin(theta)^3=-b/a^2*csc(theta)^3,%);