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The power rule is used to find the slope of polynomial functions and any other function that contains an exponent with a real number. In other words, it helps to take the derivative of a variable raised to a power (exponent).
Power function definition: A one-term function with a variable as the base and a constant as the exponent. The exponent in the case of a power function is always a constant and a real number. The general form of a power function is, f ( x ) = k x n.
The power rule in integration is ? xn dx = (xn+1) / (n+1) + C. For applying this rule, simply add 1 to the given exponent and divide by the same resultant exponent. Add a C at the end. For example, ? x5 dx = (x6) / 6 + C.
We can write the general power rule formula as the derivative of x to the power n is given by n multiplied by x to the power n minus 1. Mathematically, the general formula for the differentiation of algebraic expressions using the of power rule is given by, d(xn)/dx OR (xn)' = nxn-1, where n is a real number.
The Power Rule states that if f(x) = xn, where n is a positive integer, then f'(x) = nxn-1. Let n=1. Then f(x) = x. and f'(x) = 1, which is equal to the derivative of x.