what is differentiation?

Question

mathematics

Answer 1

It's a mathematical operation that gives you an equation for the slope of a line which can have physical meaning. For example the if you have an equation that gives a location of something as a function of time, the slope is its velocity.

Answer 2

It is a mathematical operation and part of the subject of calculus. It is a process which finds the rate of change of a variable (the dependant variable) with respect to another variable.
For example it could be the rate of change of distance with respect to time and this would be written ds/dt. The independent variable does not have to be time. Rate is the same as a gradient of a straight line and you don't have to use calculus. But if the relationship say between y and x, is a curve then rate is the tangent to the curve at any given point. Differentiation of y with respect to x is a way of getting that gradient/

Answer 3

the process of finding the derivative is called differentiation. The reverse process is integration. The two processes are the central concepts of calculus and are related via the fundamental theorem of calculus.

For real-valued functions of a single real variable the derivative gives the slope of the tangent to the graph of the function at a point. In this way, derivatives can be used to determine many properties of the function, such as whether the function has a maximum or minimum.

The concept of derivative can be extended to functions of more than one variable, to functions of complex variables and to many other cases.

Differentiation has many applications throughout all numerate disciplines. For example, in physics, the derivative of the position of moving body will give its velocity (speed) and the second derivative of the body's position gives its acceleration.

Answer 4

The computation of a derivative is known as differentiation.

The derivative of a function represents an infinitesimal change in the function with respect to one of its variables.

The "simple" derivative of a function f with respect to a variable x is denoted either f'(x) or df/dx i.e
df
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dx