Question

what is meaning of differentiation​

Answer 1

Answer:

Physical meaning of differentiation is that it represent rate of change of parameter. For example differential of velocity graph will indicate accelaration. ... Differentiation means the mesurement of rate of change of one variable with respect to other.

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Answer 2

Differentiation is a process of finding a function that outputs the rate of change of one variable with respect to another variable.

Informally, we may suppose that we're tracking the position of a car on a two-lane road with no passing lanes. Assuming the car never pulls off the road, we can abstractly study the car's position by assigning it a variable, {\displaystyle x} x . Since the car's position changes as the time changes, we say that {\displaystyle x} x is dependent on time, or {\displaystyle x=f(t)} x=f(t) . This tells where the car is at each specific time. Differentiation gives us a function {\displaystyle {\frac {dx}{dt}}} {\frac {dx}{dt}} which represents the car's speed, that is the rate of change of its position with respect to time.

Equivalently, differentiation gives us the slope at any point of the graph of a non-linear function. For a linear function, of form {\displaystyle f(x)=ax+b} f(x)=ax+b , {\displaystyle a} a is the slope. For non-linear functions, such as {\displaystyle f(x)=3x^{2}} f(x)=3x^{2} , the slope can depend on {\displaystyle x} x ; differentiation gives us a function which represents this slope