Changes

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)'''

<math>\frac{dy}{dx} = nx^{(n-1)}</math>

For example, let y = 3 x^2

For example, if <math>y = 3 x^2</math>, the derivative with respect to <math>x</math> is

Then, dy/dx = 6 x

<math>\frac{dy}{dx} = 6 x</math>

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.