Differentiation is a mathematical concept that involves finding the rate at which one variable changes in relation to another variable. It is commonly used in calculus to solve problems involving rates of change, slopes, and curves.
Differentiation allows us to analyze and understand the behavior of complex systems by breaking them down into smaller, more manageable parts. It is also essential in many fields such as physics, economics, and engineering to solve real-world problems.
The three most commonly used methods of differentiation are the power rule, product rule, and chain rule. Other methods include quotient rule, implicit differentiation, and logarithmic differentiation.
To find the derivative of a function, you can use the rules of differentiation, such as the power rule, product rule, or chain rule. Alternatively, you can also use the limit definition of a derivative, which involves taking the limit of a difference quotient as the interval between two points approaches zero.
Differentiation has numerous applications in fields such as physics, economics, engineering, and biology. Examples include finding the velocity of a moving object, maximizing profits in business, designing optimal structures, and modeling population growth.