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A differential is the result gained when mathematical differentiation is applied to a function. Differentiation in maths is the function which finds the gradient of a function in terms of x. Differentiation in biology is the specialisation of unspecialised cells such as stem cells into active cells.
Integration and differentiation effectively un-do each other. The derivative of the integral of a function is usually the original function. The reverse is also true, to a point.
Differentiation is just another way so saying find the derivative of a function.
Differentiation lets you find the rate of change of a function. You can use this to find the maximum or minimum values of a differentiable function, which is useful in a lot of optimization problems. It's also necessary for differential equations, which are useful just about everywhere.
Differentiation: when you differentiate a function, you find a new function (the derivative) which expresses the old function's rate of change. For example, if f(x) = 2x, then the derivative f ' (x) = 2 for all x, because the function is always increasing by 2 units for every increase of x by 1 unit.A differential equation is an equation expressing a relationship between a named function and its derivatives. This can be as simple as y = y', where y is the original function and y' the derivative.