Question 1123187
<pre>{{{matrix(1,3, y,""="", (x^2)/(x^2+25) )) }}} has the graph:

{{{graph(400,400*2/5,-5,5,-2,2,(x^2)/(x^2+25))}}}

It is differentiable everywhere for there are no vertical asymptotes,
or any points of discontuity.  The derivative is

{{{matrix(1,3,(dy)/(dx),""="", ((x^2+25)(2x)-x^2(2x))/(x^2+25)^2)}}}

{{{matrix(1,3,(dy)/(dx),""="",(2x^3+50x-2x^3)/(x^2+25)^2)}}}

{{{matrix(1,3,(dy)/(dx),""="",(50x^"")/(x^2+25)^2)}}}

which is defined everywhere.  "Everywhere" means 
"all real numbers" and the interval notation for
"all real numbers" is from negative infinity to
positive infinity" and is written:

{{{(matrix(1,3,-infinity,",",infinity))}}}

Edwin</pre>