Power Rule
The power rule is a fundamental concept in calculus that is used to differentiate power functions, where the variable is raised to a constant exponent
The power rule is a fundamental concept in calculus that is used to differentiate power functions, where the variable is raised to a constant exponent. The power rule states that if we have a function of the form f(x) = x^n, where n is any constant, then the derivative of f(x) can be found by multiplying the exponent n by the coefficient in front of x and subtracting 1 from the exponent.
In mathematical notation, the power rule is written as:
d/dx (x^n) = n * x^(n-1)
For example, if we have the function f(x) = 2x^3, we can find its derivative using the power rule. The derivative of f(x) with respect to x is given by:
d/dx (2x^3) = 3 * 2x^(3-1) = 6x^2
So, the derivative of 2x^3 is 6x^2.
The power rule can be applied to various types of power functions, including polynomials, rational functions, and exponential functions. It is a powerful tool in calculus that allows us to find the rate of change (slope) of a function at any point.
It is important to note that the power rule only applies when the exponent is a constant. If the exponent is not a constant, or if it involves functions other than x, additional rules like the chain rule or product rule may be required to find the derivative.
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