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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, 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.

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)'''

Thus the '''derivative''' is a measurement of how a function changes when the values of its inputs vary. Having calculated the derivative, the original input (in the above example, x) can be substituted in to work out the gradient. Moreover, differentiation can be employed to calculate the maxima and minima of a function (e.g. to ascertain the maximum velocity of an object in a function defining how its displacement varies with time), whereby dy/dx=0.

Thus the '''[[derivative]]''' is a measurement of how a function changes when the values of its inputs vary. Having calculated the derivative, the original input (in the above example, x) can be substituted in to work out the gradient. Moreover, differentiation can be employed to calculate the maxima and minima of a function (e.g. to ascertain the maximum velocity of an object in a function defining how its displacement varies with time), whereby dy/dx=0.

===Differentiation Rules===

===Differentiation Rules===