Difference between revisions 26979084 and 26979180 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]].

===Example 2===
Consider the graph of <math>f(x)=2x-3</math>. If the reader has an understanding of [[algebra]] and the [[Cartesian coordinate system]], the reader should be able to independently determine that this [[line (mathematics)|line]] has a slope of 2 at every point. Using the above quotient (along with an understanding of the [[limit (mathematics)|limit]], [[secant]], and [[tangent]]) one can determine the slope at (4,5):

:{|
|-
(contracted; show full)|-
|
|<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]]