Question

Why do we Differentiate?

Answer 1

Differentiation:

1. The differentiation of a function is the process of finding its derivative.
2. The derivative of a function gives the rate of change of the function.
3. Differentiating a function with respect to a variable determines how the variable affects the function.

Uses of differentiation:

1. Differentiation is used to determine the instantaneous rate of change of quantities.
2. For instance, if we want to find the velocity of a car, we can do it by using differentiation. Mathematically, it is expressed as $v=\frac{ds}{dt}$, where $s$ is displacement an. is time.
3. It is used to find the trend of a quantity, whether it is increasing, decreasing or constant. Therefore, they can be used in market research.
4. It is also used to derive various equations and find the slope of a curve.

Hence, differentiation is used for various purposes like market research, finding the rate of change of quantities, and many more.