Difference between revisions 19577355 and 19577916 on enwiki

< previous diff
next diff >
Derivative (examples)
===Example 1===
Consider ''f''(''x'') = 5:

: <math>f'(x)=\lim_{h\rightarrow 0} \frac{f(x+h)-f(x)}{h} = \lim_{h\rightarrow 0} \frac{5-5}{h} = 0</math>

The derivative of a [[constant]] is [[0 (number)|zero]].

===Example 2===
(contracted; show full)
::<math> = \lim_{h\rightarrow 0} \frac{\frac{x}{\sqrt{x} \sqrt{x+h}}-\frac{x+h}{\sqrt{x} \sqrt{x+h}}}{h(2 \sqrt{x+h}+2 \sqrt{x})}</math>
::<math> = \lim_{h\rightarrow 0} \frac{\frac{h}{\sqrt{x} \sqrt{x+h}}}{h(2 \sqrt{x+h}+2 \sqrt{x})}</math>
::<math> = \lim_{h\rightarrow 0} \frac{1}{\sqrt{x} \sqrt{x+h} (2 \sqrt{x+h}+2 \sqrt{x})}</math>
::<math> = \lim_{h\rightarrow 0} \frac{1}{2 \sqrt{x} (x+h) + 2 x \sqrt{x+h}}</math>
::<math> =
 \lim_{h\rightarrow 0} \frac{1}{4 x \sqrt{x}}</math>