d/dx [x^n] (Power Rule)
The power rule is a fundamental rule used in calculus to find the derivative of a function involving a variable raised to a power
The power rule is a fundamental rule used in calculus to find the derivative of a function involving a variable raised to a power. In particular, for a given function f(x) = x^n, where n is a constant, the derivative of this function, denoted as d/dx [x^n], can be found using the power rule.
The power rule states that if we have a function f(x) = x^n, then the derivative with respect to x, d/dx [x^n], is given by:
d/dx [x^n] = n * x^(n-1)
The power rule tells us that when differentiating a term with the variable x raised to a constant power n, we can bring down the power as the coefficient and decrease the power by 1.
For example, if we have f(x) = x^3, applying the power rule gives us:
d/dx [x^3] = 3 * x^(3-1) = 3 * x^2
Similarly, for f(x) = x^4, the derivative is:
d/dx [x^4] = 4 * x^(4-1) = 4 * x^3
This rule is applicable to any constant power n. It is important to note that the power rule holds true for any constant value of n, except when n = 0. In the case where n = 0, the function becomes a constant and its derivative is zero.
More Answers:
[next_post_link]