Guided Example #3 - Definition of Deriviative

Find the derivative of the following function using the definition of derivative. $f (x) = x^{2}$

A. $2 x$ B. $2 x + c$ C. $2$ D. $0$

$lim_{x \to \infty} (\frac{3 x^{2} - x + 10}{2 x - 1})$

$f' (x) = lim_{h \to o} (2 x + h) = 2 x$

$f' (x) = lim_{h \to o} \frac{{(x + h)}^{2} - x^{2}}{h}$

$f' (x) = lim_{h \to o} \frac{x^{2} + 2 x h + h^{2} - x^{2}}{h}$

$f' (x) = lim_{h \to o} \frac{2 x h + h^{2}}{h}$

$f' (x) = lim_{h \to o} (2 x + h) = 2 x$

$f' (x) = lim_{h \to o} (2 x + h) = 2 x$

$f' (x) = lim_{h \to o} \frac{{(x + h)}^{2} - x^{2}}{h}$

$f' (x) = lim_{h \to o} \frac{x^{2} + 2 x h + h^{2} - x^{2}}{h}$

$f' (x) = lim_{h \to o} \frac{2 x h + h^{2}}{h}$

$f' (x) = lim_{h \to o} (2 x + h) = 2 x$