Understanding the Power Rule | Finding the Derivative of a Single Variable Function f(x) = 2x

derivative of a single variable, f(x)=2x

The derivative of a function with respect to a single variable measures how the function changes as the inputs to the function change

The derivative of a function with respect to a single variable measures how the function changes as the inputs to the function change. In other words, it captures the rate at which the function is changing for any given input value.

To find the derivative of a single variable function f(x), we can use the power rule, which states that if f(x) = x^n, where n is a constant, then the derivative of f(x) with respect to x is given by:

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

In the case of the function f(x) = 2x, we can rewrite it as f(x) = 2x^1, where n = 1. Applying the power rule, we find that the derivative of f(x) is:

f'(x) = 1*(2x)^(1-1) = 2x^0 = 2

So, the derivative of f(x) = 2x is f'(x) = 2.

This means that for any value of x, the rate of change of the function f(x) = 2x is always 2.

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