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The power function is a mathematical function of the form f(x) = ax^b, where a and b are constants.

To derive the power function, we start with the general form of a function:

f(x) = ax^b

To find the derivative of this function, we use the power rule of differentiation. According to the power rule, the derivative of x^n with respect to x is nx^(n-1), where n is any real number.

Applying the power rule to the function f(x) = ax^b, we have:

f'(x) = d/dx(ax^b)

= abx^(b-1)

Therefore, the derivative of the power function f(x) = ax^b is f'(x) = abx^(b-1).

To derive the power function, we start with the general form of a function:

f(x) = ax^b

To find the derivative of this function, we use the power rule of differentiation. According to the power rule, the derivative of x^n with respect to x is nx^(n-1), where n is any real number.

Applying the power rule to the function f(x) = ax^b, we have:

f'(x) = d/dx(ax^b)

= abx^(b-1)

Therefore, the derivative of the power function f(x) = ax^b is f'(x) = abx^(b-1).

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