To find the derivative of the function 2x, you can apply the power rule of differentiation. The power rule states that if you have a term of the form ax^n, where a is a constant and n is a positive integer, the derivative is n * ax^(n-1).
In the case of 2x, we can rewrite it as 2x^1. Here, the constant a is 2 and n is 1. Applying the power rule:
- Multiply the exponent (1) by the coefficient (2): 1 * 2 = 2.
- Then, reduce the exponent by 1: 1 – 1 = 0.
Thus, the derivative of 2x is 2x^0, and since any number to the power of 0 is 1, we simplify this to:
2
So, the derivative of 2x is 2.