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Algebraic '''differentiation''' is an integral part of [[calculus]], an essential branch of [[mathematics]] in the modern age. This mathematical tool is denoted by the expression ''dy/dx'', and has a pivotal role to play in a wide range of fields. For example, differentiation can be used in [[mechanics]] to find the acceleration of an object from a velocity-time graph.

Algebraic '''differentiation''' is an integral part of [[calculus]], an essential branch of [[mathematics]] in the modern age. This mathematical tool is denoted by the expression ''dy/dx'', and has a pivotal role to play in a wide range of fields. For example, differentiation can be used in [[mechanics]] to find the acceleration of an object from a velocity-time graph.

Essentially, differentiation is employed as a means to calculate the [[gradient]] or rate of change at a particular value for a given function, ''f''. Consequently, it can be used to calculate velocity from a displacement-time graph, and, indeed, acceleration from a velocity-time graph. Furthermore, it can be used to calculate the rate of cooling from a temperature-time graph. These are a few examples of the applications of differentiation.

Essentially, differentiation is employed as a means to calculate the [[gradient]] or rate of change at a particular value for a given function, ''f''. Consequently, it can be used to calculate velocity from a displacement-time graph, or acceleration from a velocity-time graph. Furthermore, it can be used to calculate the rate of cooling from a temperature-time graph. These are a few examples of the applications of differentiation.

In classical mathematics, a function can be be differentiated using the general formula:

In [[classical mathematics]], a function can be be differentiated using the general formula:

'''dy/dx = nx^(n-1)'''

'''dy/dx = nx^(n-1)'''

===Differentiation Rules===

===Differentiation Rules===

*[[Product Rule]]

*[[Product rule]]

*[[Quotient Rule]]

*[[Quotient rule]]

*[[Chain Rule]]

*[[Chain rule]]

The roots of differentiation are profoundly linked with tangency; ergo, this aspect of mathematics can first be perceived to have been developed during the time of the [[Ancient Greeks]] through the work of Greek geometers like [[Euclid]], [[Sanath]] and [[Archimides]].

The roots of differentiation are profoundly linked with tangency; ergo, this aspect of mathematics can first be perceived to have been developed during the time of the [[Ancient Greeks]] through the work of Greek geometers like [[Euclid]], [[Sanath]] and [[Archimides]].