Differentiation is a mathematical process used to find the derivative, or rate of change, of a function. It is a fundamental tool of calculus. The derivative shows the sensitivity of change of a functions output with respect to the input. Differentiation can be carried out by purely algebraic manipulations, using three basic derivatives, four rules of operation, and a knowledge of how to manipulate functions. The three basic derivatives are:
- For algebraic functions, D(x^n) = nx^(n-1), where n is any real number.
- For trigonometric functions, D(sin x) = cos x and D(cos x) = -sin x.
- For exponential functions, D(e^x) = e^x.
The theory provides basic rules for differentiating the sum, product, or quotient of any two functions f(x) and g(x) the derivatives of which are known. Differentiation is a process of finding the instantaneous rate of change in a function based on one of its variables. It can be applied to measure the function per unit change in the independent variable. The meaning of differentiation is the process of determining the derivative of a function at any point. Linear and non-linear functions are generally classified under calculus.
