Mastering the Power Rule | Simplify Calculus Derivatives of Power Functions

What is the power rule?

The power rule is a formula used in calculus to find the derivative of a function that is in the form of a power of x

The power rule is a formula used in calculus to find the derivative of a function that is in the form of a power of x. The rule states that if a function is defined as f(x) = x^n, where n is a constant, the derivative of the function, denoted as f'(x) or dy/dx, is found by multiplying the constant n by the coefficient of x, and then subtracting 1 from the exponent.

Mathematically, the power rule can be expressed as follows:

f(x) = x^n

f'(x) = n * x^(n-1)

For example, let’s say we have the function f(x) = x^3. Applying the power rule, we differentiate the function by multiplying the coefficient 3 by the exponent 3, which gives us 9. Then we subtract 1 from the exponent to get 3-1=2. Therefore, the derivative of f(x) = x^3 is f'(x) = 3x^2.

The power rule can be applied to functions of any power of x, such as f(x) = x^2, f(x) = x^4, or even f(x) = x^(-2). However, it is important to note that the power rule is only applicable to functions where the exponent is a constant.

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