derivative power rule
x^n = nx^n-1
The power rule is a formula used to find the derivative of a function in the form f(x) = x^n, where n is a constant.
The power rule states that:
– If f(x) = x^n, then f'(x) = nx^(n-1), where f'(x) represents the derivative of f(x).
This means that when taking the derivative of a function in the form of x^n, we can simply multiply the original exponent by the coefficient of x and then subtract 1 from the original exponent.
For example, let’s say we want to find the derivative of the function f(x) = 5x^4. Using the power rule, we can write:
f'(x) = 5 * 4x^(4-1)
f'(x) = 20x^3
Therefore, the derivative of f(x) = 5x^4 is f'(x) = 20x^3 using the power rule.
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