Difference between revisions 30006624 and 30238943 on enwiki

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Derivative (examples)
{{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]].
(contracted; show full)|<math> = \lim_{h\rightarrow 0} \frac{-1}{\sqrt{x} \sqrt{x+h} (2 \sqrt{x+h}+2 \sqrt{x})}</math>
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|<math> = \lim_{h\rightarrow 0} \frac{-1}{2 \sqrt{x} (x+h) + 2 x \sqrt{x+h}}</math>
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|<math> = \frac{-1}{4 x \sqrt{x}}</math>
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|<math> = \frac{1}{4 x \sqrt{x}}</math> 
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(<math>\sqrt{x}</math> has 2 answers that only differ in sign, so it doesn't matter which sign we put in front of the end result.)}

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

[[fr:Exemples de calcul de dérivée]]