Question 1010270
{{{f(x+h)=(x+h)^2+(x+h)=x^2+2xh+h^2+x+h=x^2+(2h+1)x+(h^2+h)}}}
{{{f(x+h)-f(x)=x^2+(2h+1)x+(h^2+h)-x^2+x=2hx+h^2+h}}}
{{{(f(x+h)-f(x))/h=2x+h+1}}}
So then,
{{{df/dx=lim(h->0,(2x+h+1))=2x+1}}}