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Using the definition of a derivative how do you calculate the derivative of $f (x) = x^{2} + x$ $f(x) = x^2 + x$ ?

1 Answer

May 18, 2015

$lim_{h->0}(f(x+h)-f(x))/h=lim_{h->0}((x+h)^2+(x+h)-x^2-x)/h$

$=lim_{h->0}(x^2+2xh+h^2+h-x^2)/h=lim_{h->0}(h(2x+h+1))/h$

$=lim_{h->0}(2x+1+h)=2x+1$ .

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