# What is the derivative of pi?

Mar 3, 2018

$0$; Derivative of a constant is always $0$

#### Explanation:

The derivative of a constant term is always zero. Reason being, we take derivatives with respect to a variable.

We understand derivatives to be the slope of the tangent line, or our instantaneous rate of change. Take the following derivative:

$\frac{d}{\mathrm{dx}} \left[2 x + 8\right] = 2$

This expression that we're taking the derivative of is in slope-intercept form ($y = m x + b$), where $m$ is the slope. In our case, the slope is $2$, so the derivative is $2$.

Remember, $\frac{d}{\mathrm{dx}}$ means we're taking the derivative with respect to $x$, or how much $y$ changes with respect to $x$. $\pi$ is just a constant, meaning it doesn't change with respect to a variable . It will graph as a horizontal line, just like $2 , 8 ,$and $11$ will. As we know, slopes of horizontal lines are $0$, so the derivative of a constant, like $\pi$, will always be zero.