Difference between revisions of "Derivative/Definition"

Revision as of 15:55, 3 March 2010

Differential Calculus is a sub-field of Calculus that primarily focuses on how functions change as the input changes. In Differential Calculus we usually use Differentiation, or the process of finding the derivative.

Derivative represents the slope of the slope of the line tangent to a function at some point.

Long method for Derivative: Let the function be $ax^n+bx^{n-1}+cx^{n-2}+....z=0$ . Find the First Derivate

$\boxed{\text{Solution:}}$

@@ Line 1: / Line 1: @@
-The [[derivative]] of a [[function]] is defined as the instantaneous rate of change of the function at a certain [[point]].  For a [[line]], this is just the [[slope]].  For more complex [[curves]], we can find the rate of change between two points on the curve easily since we can draw a line through them.
+Differential Calculus is a sub-field of Calculus that primarily focuses on how functions change as the input changes. In Differential Calculus we usually use Differentiation, or the process of finding the derivative.
-<center>[[Image:derivative1.PNG]]</center>
+Derivative represents the slope of the slope of the line tangent to a function at some point.
-In the image above, the average rate of change between the two points is the slope of the line that goes through them: <math>\frac{f(x+h)-f(x)}h</math>.
+Long method for Derivative: Let the function be <math>ax^n+bx^{n-1}+cx^{n-2}+....z=0</math>. Find the First Derivate
-We can move the second point closer to the first one to find a more accurate value of the derivative.  Thus, taking the [[limit]] as <math>h</math> goes to 0 will give us the derivative of the function at <math>x</math>:
+<math>\boxed{\text{Solution:}}</math>
-<center>[[Image:derivative2.PNG]]</center>
-<center><math> f'(x) = \lim_{h\to 0}\frac{f(x+h)-f(x)}h. </math></center>
-If this limit exists, it is the derivative of <math>f</math> at <math>x</math>. If it does not exist, we say that <math>f</math> is not differentiable at <math>x</math>.
-== See also ==
-* [[Calculus]]
-* [[Derivative]]
-[[Category:Calculus]]

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Difference between revisions of "Derivative/Definition"

Revision as of 15:55, 3 March 2010