Answer: The power rule is a simple and widely used rule for finding the derivative of a power function. Specifically, the power rule states that if f(x) = x^n, where n is a constant, then the derivative of f(x) with respect to x is:
f'(x) = n * x^(n-1)
In other words, to find the derivative of a power function, you can follow these steps:
Identify the power function: Make sure the function you want to differentiate is in the form of x raised to some constant power, i.e., f(x) = x^n.
Subtract one from the exponent: Take the exponent of x, subtract one from it, and write the result as the new exponent. That is, n becomes (n-1).
Multiply by the original exponent: Multiply the result from step 2 by the original exponent of x, n. This gives you the derivative of the power function.
For example, if you have the function f(x) = x^3, you can use the power rule to find the derivative:
f'(x) = 3 * x^(3-1)
= 3 * x^2
Therefore, the derivative of f(x) = x^3 is f'(x) = 3x^2.
Note that the power rule applies only to power functions, and there are other rules for finding the derivatives of other types of functions.
Explanation: