10 Hard Math Problems That May Never Be Solved - Free Printable

- The image displays the definition of the derivative using the limit process: $f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$.
- It shows a specific example, likely for $f(x) = x^2$, where the difference quotient $\frac{(x+h)^2 - x^2}{h}$ is expanded to $\frac{x^2 + 2xh + h^2 - x^2}{h}$.
- This simplifies to $\frac{2xh + h^2}{h}$, and then to $2x + h$ after canceling $h$ (for $h \neq 0$).
- Taking the limit as $h \to 0$ yields the derivative $f'(x) = 2x$.
- The general power rule $\frac{d}{dx}(x^n) = nx^{n-1}$ is also shown, which is consistent with the result for $n=2$.