Question 964913
{{{f(x)=-4x^2+9x+2}}}
{{{f(x+h)=-4(x+h)^2+9(x+h)+2}}}
{{{f(x+h)=-4(x^2+2xh+h^2)+9x+9h+2}}}
{{{f(x+h)=-4x^2-8xh-4h^2+9x+9h+2}}}
{{{f(x+h)=-4x^2+9x-8hx-4h^2+9h+2}}}
{{{f(x+h)-f(x)=-4x^2+9x-8hx-4h^2+9h+2+4x^2-9x-2}}}
{{{f(x+h)-f(x)=-8hx-4h^2+9h}}}
{{{(f(x+h)-f(x))/h=-8x-4h+9}}}
{{{lim(x->0,((f(x+h)-f(x))/h))=-8x+9}}}
{{{df/dx=-8x+9}}}
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{{{f(x)=x/(x+1)}}}
{{{f(x+h)=(x+h)/(x+h+1)}}}
{{{f(x+h)-f(x)=(x+h)/(x+h+1)-x/(x+1)}}}
{{{f(x+h)-f(x)=((x+h)(x+1))/((x+h+1)(x+1))-(x(x+h+1))/((x+h+1)(x+1))}}}
{{{f(x+h)-f(x)=((x+h)(x+1)-(x(x+h+1)))/((x+h+1)(x+1))}}}
{{{f(x+h)-f(x)=(x^2+x+hx+h-(x^2+hx+x))/((x+h+1)(x+1))}}}
{{{f(x+h)-f(x)=(x^2+x+hx+h-x^2-hx-x))/((x+h+1)(x+1))}}}
{{{f(x+h)-f(x)=(h))/((x+h+1)(x+1))}}}
{{{(f(x+h)-f(x))/h=1/((x+h+1)(x+1))}}}
{{{lim(x->0,((f(x+h)-f(x))/h))=1/(x+1)^2}}}
{{{df/dx=1/(x+1)^2}}}