Differentiation rules for functions from "summary" of Differential Calculus by S Balachandra Rao
Differentiation rules for functions are fundamental tools in calculus that allow us to find the derivative of a wide variety of functions. These rules provide a systematic way to differentiate functions without having to resort to first principles every time. By applying these rules, we can determine the rate of change of a function at any point, which is crucial in many real-world applications. The power rule is one of the most basic differentiation rules and is used to find the derivative of a function raised to a constant power. For example, if we have a function f(x) = x^n, where n is a constant, then the derivative of f(x) with respect to x is n*x^(n-1). This rule simplifies the process of finding derivatives of polynomials and other functions with exponents. Another important rule is the sum rule, which states that the derivative of a sum of functions is equal to the sum of the derivatives of the individual functions. This rule allows us to break down complex functions into si...
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