Some derivatives and limits with Maple

> f:=sqrt(x^2-4)/(x^3+2);

f := (x^2-4)^(1/2)/(x^3+2)

> g:=diff(f,x);

g := 1/(x^2-4)^(1/2)/(x^3+2)*x-3*(x^2-4)^(1/2)/(x^3...

> h:=simplify(g);

h := -2*x*(x^3-1-6*x)/(x^2-4)^(1/2)/(x^3+2)^2

> simplify(g-h);

0

> f:=cos(cos(cos(x)));

f := cos(cos(cos(x)))

> g:=diff(f,x);

g := -sin(cos(cos(x)))*sin(cos(x))*sin(x)

> f:=sin(10*x)/sin(9*x);

f := sin(10*x)/sin(9*x)

> limit(f,x=0);

10/9

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