Difference between revisions 74294721 and 80877183 on enwiki

:''For more background on this topic, see [[derivative]].''

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

The derivative of a [[constant function]] is [[0 (number)|zero]].
(contracted; show full)|<math> f'(x)\, </math>
|<math>= \lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h} </math>
|-
|
|<math> = \lim_{h\rightarrow 0}\frac{\sqrt{x+h} - \sqrt{x}}{h} </math>
|-
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|<math> = \lim_{h\rightarrow 0}\
left(\frac{(\sqrt{x+h} - \sqrt{x})(}{h}\right) \left(\frac{\sqrt{x+h} + \sqrt{x})}{h(\sqrt{x+h} + \sqrt{x})}\right) </math>
|-
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|<math> = \lim_{h\rightarrow 0}\frac{x+h - x}{h(\sqrt{x+h} + \sqrt{x})} </math>
|-
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|<math> = \lim_{h\rightarrow 0}\frac{1}{\sqrt{x+h} + \sqrt{x}} </math>
|-
(contracted; show full)|
|<math> = \frac{-1}{4 x \sqrt{x}}</math>
|}

[[Category:calculus]] [[Category:Mathematical notation]]

[[eo:Derivaĵo (ekzemploj)]]
[[fr:Exemples de calcul de dérivée]]