**Definition of Differentiation:**

- Differentiation is the extract of basic calculus in mathematics. It is also called derivative.
- It is defined as the change of a function with respect to one of the variables involved.
- By using basic principle of differentiation or derivative we find out instantaneous change with respect of any of the variable involved.

**Explanation of Differentiation:**

- The approach of differentiation is used when we need to calculate the rate of change in a quantity with respect to time or any independent quantity.
- Derivative is also termed as slope or tangent of a function.
- If x and y are real numbers and we plot a graph of function f(x) across x axis. Now within a graph it is calculated as ratio of rise to run or y coordinate (value in y axis) to x coordinate (value in x axis).

**Examples of Differentiation:**

- Velocity is a derivative of displacement which means velocity is change in displacement with respect to fractional change in time. E.g. v=dx/dt
- While acceleration is the change in velocity with respect to time interval which passed during that change.
- The differentiation equation for acceleration is a=dv/dt
- Another example of derivative of a function through graph. Let us suppose a function with independent variable x and dependent variable y. suppose it is y= f(x) and f(x) be the function of variable. Now we have to find change in y or f(x) with respect to change in x.
- The differentiation calculator for this function can be formulated by formulating dy=y2-y1 and dx=x2-x1 slope, tangent or derivative through graph can be calculated as slope=dy/dx.

Slope = (y2-y1)/(x2-x1)

**Applications of Differentiation:**

The concept of differentiation is not only used in mathematics, differentiation calculator is used in finance economics business and engineering. Whenever we require to calculate constantly varying quantities we require differentiation equation. In business it is used to calculate cost reduction and profit increase. While in engineering differentiation is required to calculate maximum strength and minimum cost.

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