Power Rule
d/dx (axⁿ) = naxⁿ⁻¹
The power rule is a method used in calculus to differentiate a function of the form f(x) = x^n, where n is any real number. The rule states that the derivative of this function is f'(x) = n*x^(n-1).
For example, if we have the function f(x) = x^3, the power rule tells us that its derivative is f'(x) = 3*x^2.
This rule is useful in many situations where we need to find the slope of a curve or the rate of change of a function. It is also used in engineering, physics, and other areas of science to model and analyze complex systems.
It is important to note that the power rule only applies to functions of this specific form, and cannot be used for more complex functions. Additionally, when using the power rule, it is always best to check your answer by taking the second derivative to ensure that you have the correct solution.
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