What is the Derivative of 2x?

A derivative measures the rate of change of a function at a specific point. It tells us how much the function’s value changes as the input changes. In simpler terms, it’s like determining the slope of a curve at a particular point. In this article, we will explore the derivative of the simple function 2x and its significance.

Answer: The derivative of 2x is 2.

Now, let’s find the derivative of the function 2x. The derivative is represented as f'(x) or dy/dx, where ‘f’ is the function, and ‘x’ is the input variable. In our case, f(x) = 2x.

To calculate the derivative, we can use a simple rule: “Power Rule.” The Power Rule states that if you have a function f(x) = axⁿ, where ‘a’ and ‘n’ are constants, then its derivative f'(x) is given by:

f'(x) = n. a . x^(n-1)

In our case, a = 2 and n = 1 (since x is raised to the power of 1).

Applying the Power Rule:

f'(x) = 1. 2 .x^(1-1) = 2.x⁰= 2 .1 = 2

So, the derivative of 2x is simply 2.

Now that we know the derivative of 2x is 2, what does it signify? It tells us that for the function f(x) = 2x, the rate of change at any point is constant and equal to 2. In other words, as ‘x’ increases or decreases, the function 2x changes at a steady rate of 2 units for every unit change in ‘x.’