Difference between revisions 80877183 and 81350941 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> = \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>.

===Example 4===
Consider 
''f''(''x'') = √''x''<math> f(x) = \sqrt{x} </math>:

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