Question

What is the derivative of $2x$?

Answer 1

A function that denotes the rate of change of the other function can be called the derivative of that function.

Derivative formula:

• $\frac{d}{dx}\left(af\left(x\right)\right)=a\frac{d}{dx}\left(f\left(x\right)\right)$, where $a$ is a constant.
• $\frac{dx}{dx}=1$

Given function is $f\left(x\right)=2x$.

Differentiate the function with respect to $x$, we get

$\frac{d}{dx}f\left(x\right)=\frac{d}{dx}\left(2x\right)$

$\Rightarrow$ $\frac{d}{dx}f\left(x\right)=2\frac{dx}{dx}$

$\Rightarrow$ $\frac{d}{dx}f\left(x\right)=2$

Hence, the derivative of $2x$ is $2$.