Difference between revisions 34832353 and 35044743 on enwiki

{{background|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{5-5}{h} = 0</math>

The derivative of a [[constant function]] is [[0 (number)|zero]].
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|<math> = \lim_{h\rightarrow 0}(2x + h) = 2x </math>
|}

For any point ''x'', the slope of the function <math>f(x)=x^2</math> is <math>f'(x)=2x</math>.


<math>Insert formula here</math>
== Headline text ==
'''Bold text'''
----⏎
===Example 4===
Consider ''f''(''x'') = &radic;''x'':

:{|
|-
|<math> f'(x)\, </math>
|<math>= \lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h} </math>
|-
|j jfdirkp[jdi]
|<math> = \lim_{h\rightarrow 0}\frac{\sqrt{x+h} - \sqrt{x}}{h} </math>
|-
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|<math> = \lim_{h\rightarrow 0}\frac{(\sqrt{x+h} - \sqrt{x})(\sqrt{x+h} + \sqrt{x})}{h(\sqrt{x+h} + \sqrt{x})} </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> = \frac{-1}{4 x \sqrt{x}}</math>
|}

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

[[fr:Exemples de calcul de dérivée]]