- #1
tonyviet
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1.
f(x)= ax^2 = ae^TR, nez
Prove f '(x) = a(n) x^(n-1)2.
n does not equal 03.
I don't even understand it
f(x)= ax^2 = ae^TR, nez
Prove f '(x) = a(n) x^(n-1)2.
n does not equal 03.
I don't even understand it
Last edited:
The derivative of a function is defined as the rate of change of the function at a specific point. It represents the slope of the tangent line to the function at that point.
The power rule states that the derivative of a function raised to a power is equal to the power multiplied by the function raised to the power minus one. In other words, the derivative of f(x)^n is n*f(x)^(n-1).
Sure, let's take the function f(x) = 3x^2. Using the power rule, we know that f'(x) = 2*3x^(2-1) = 6x. Therefore, we have proved that f'(x) = 6x, which is equal to a(2) x^(2-1).
The general formula for the power rule is f'(x) = n*a(n) x^(n-1), where n is the power to which the function is raised and a(n) is the coefficient in front of the function.
Yes, there are some exceptions to the power rule, such as when the function is a constant or when the function is raised to a negative power. In these cases, a different method must be used to find the derivative.