Power Rule
The power rule is a fundamental rule in calculus that is used to find the derivative of a function that is in the form of a power function
The power rule is a fundamental rule in calculus that is used to find the derivative of a function that is in the form of a power function.
The power rule states that if we have a function f(x) = x^n, where n is a constant, then its derivative is given by f'(x) = nx^(n-1).
To apply the power rule, we simply bring down the exponent as the coefficient in front of the variable, and then reduce the exponent by 1. For example, if we have the function f(x) = 3x^2, we apply the power rule by bringing down the exponent 2 as the coefficient (2 * 3) and reducing the exponent by 1 (2 – 1), which gives us the derivative f'(x) = 6x.
The power rule can be applied to any real number exponent, including positive, negative, and fractional exponents. For instance, if we have the function f(x) = x^-3, we again bring down the exponent -3 as the coefficient (-3 * x^-3) and reduce the exponent by 1 (-3 – 1), resulting in the derivative f'(x) = -3x^-4.
It is worth mentioning that the power rule is derived from the concept of the limit and the definition of the derivative. It provides a quick and efficient method for finding the derivative of power functions, which are quite common in mathematical models and real-world applications.
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