Basic Derivative Results
If $$y = f(x)$$, then
1) $$\frac{{dy}}{{dx}} = f'(x) = \mathop {\lim }\limits_{h \to 0} \frac{{f(x + h) – f(x)}}{h}$$
2) $$f'(x) = \mathop {\lim }\limits_{h \to 0} \frac{{f(a + h) – f(a)}}{h} = \mathop {\lim }\limits_{x \to a} \frac{{f(x) – f(a)}}{{x – a}}$$
3) $$L.H.D = f'(a – 0) = \mathop {\lim }\limits_{h \to 0 – 0} \frac{{f(a + h) – f(a)}}{h} = \mathop {\lim }\limits_{h \to 0} \frac{{f(a – h) – f(a)}}{{ – h}}$$
4) $$R.H.D = f'(a + 0) = \mathop {\lim }\limits_{h \to 0 + 0} \frac{{f(a + h) – f(a)}}{h} = \mathop {\lim }\limits_{h \to 0} \frac{{f(a + h) – f(a)}}{h}$$
Dan
October 13 @ 6:11 am
What is the difference between formulas 1) and 2) and which one would you use?