Difference between revisions 34824332 and 34832353 on enwiki

< previous diff
next diff >
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>
|-
|
|<math> = \lim_{h\rightarrow 0} \frac{-1}{2 \sqrt{x} (x+h) + 2 x \sqrt{x+h}}</math>
|-
|
|<math> = \frac{-1}{4 x \sqrt{x}}</math>

|-
|
|<math> = \frac{1}{4 x \sqrt{x}}</math> (<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]]