Co-Authored By:

**Differentiation**is the action of computinga

**derivative**. The

**derivative**of a function y = f(x)ofa variable x is a measure of the rate at which the value y ofthefunction changes with respect to the change of the variable x.Itis called the

**derivative**of f with respecttox.

Similarly, it is asked, what is differentiation and derivatives?

**Differentiation** is the algebraic method offindingthe **derivative** for a function at any point.The**derivative** is a concept that is at the root ofcalculus.There are two ways of introducing this concept, thegeometrical way(as the slope of a curve), and the physical way (asa rate ofchange).

**differentiate**many functions easily. If y =somefunction of x (in other words if y is equal to anexpressioncontaining numbers and x's), then the

**derivative**of y (withrespect to x) is written dy/dx, pronounced "dee y by deex".

Also know, how do you find the derivative?

**Basically, we can compute the derivative of f(x) usingthelimit definition of derivatives with the followingsteps:**

- Find f(x + h).
- Plug f(x + h), f(x), and h into the limit definition ofaderivative.
- Simplify the difference quotient.
- Take the limit, as h approaches 0, of the simplifieddifferencequotient.

**Rules for differentiation**

- General rule for differentiation:
- The derivative of a constant is equal to zero.
- The derivative of a constant multiplied by a function isequalto the constant multiplied by the derivative of thefunction.
- The derivative of a sum is equal to the sum ofthederivatives.