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To find the derivative of $f(x)=x^2$, substitute into the difference quotient to get $\frac{(x+h)^2-x^2}{h}$. Expanding the numerator yields $2xh+h^2$.

Conditions: $f(x)=x^2$.; $h$ is nonzero during the cancellation step.; The limit is taken as $h \to 0$ after simplification.

To find the derivative of $f(x)=x^2$, substitute into the difference quotient to get $\frac{(x+h)^2-x^2}{h}$. Expanding the numerator yields $2xh+h^2$.

Conditions: $f(x)=x^2$.; $h$ is nonzero during the cancellation step.; The limit is taken as $h \to 0$ after simplification.