Power Rule
x^n = nx^n-1
The power rule is a formula used in calculus to differentiate functions of the form f(x) = x^n, where n is a constant exponent. The power rule states that the derivative of x^n with respect to x is n*x^(n-1).
In other words, if we have a function f(x) = x^n, then we can find its derivative f'(x) as follows:
f'(x) = n*x^(n-1)
For example, if we have the function f(x) = x^3, its derivative f'(x) is:
f'(x) = 3x^2
Similarly, if we have the function g(x) = x^4, its derivative g'(x) is:
g'(x) = 4x^3
The power rule is a useful and frequently used tool in calculus, as many functions can be expressed in terms of powers of x. By using the power rule, we can quickly and easily find the derivative of a wide range of functions.
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