**Differentiation in Mathematics (Maths) Class 11**

Differentiation is a fundamental concept in calculus, particularly in mathematics (Maths) Class 11. It is the process of finding the derivative of a function. The derivative represents the rate of change of a function at any given point. Understanding differentiation is crucial as it helps in solving various mathematical problems, such as finding slopes of tangent lines, determining maximum and minimum values, and analyzing the behavior of functions.

**1. Definition of Differentiation:**

Differentiation can be defined as the process of computing the rate at which a function changes as its input variable, also known as the independent variable, changes. It involves finding the derivative of a function with respect to the independent variable.

**2. Derivative of a Function:**

The derivative of a function, denoted as f'(x) or dy/dx, represents the rate of change of the function with respect to the independent variable x. It can be calculated using various differentiation rules and formulas, such as the power rule, product rule, quotient rule, and chain rule.

**3. Differentiation Rules:**

- Power Rule: The power rule states that if f(x) = x^n, where n is a constant, then the derivative of f(x) is given by f'(x) = nx^(n-1).
- Product Rule: The product rule states that if f(x) = u(x)v(x), where u(x) and v(x) are functions of x, then the derivative of f(x) is given by f'(x) = u'(x)v(x) + u(x)v'(x).
- Quotient Rule: The quotient rule states that if f(x) = u(x)/v(x), where u(x) and v(x) are functions of x, then the derivative of f(x) is given by f'(x) = (u'(x)v(x) - u(x)v'(x))/[v(x)]^2.
- Chain Rule: The chain rule states that if f(x) = g(h(x)), where g(x) and h(x) are functions of x, then the derivative of f(x) is given by f'(x) = g'(h(x))h'(x).

**4. Applications of Differentiation:**

Differentiation is widely used in various fields of mathematics, science, and engineering. Some of the applications of differentiation include:

- Finding slopes of tangent lines and rates of change.
- Determining maximum and minimum values of functions.
- Analyzing the behavior of functions and studying their concavity and inflection points.
- Solving optimization problems and finding the maximum or minimum values of quantities.
- Calculating velocities and accelerations in physics.

In conclusion, differentiation is a fundamental concept in mathematics (Maths) Class 11. It involves finding the derivative of a function to determine its rate of change. Differentiation rules and formulas are used to calculate derivatives, and it has numerous applications in various fields. Understanding differentiation is essential for solving mathematical problems and analyzing the behavior of functions.