Question

What is the derivative of `mx+b`?

Answer 1

Considering the function (linear): `y=mx+b` where m and b are real numbers, the derivative, `y'`, of this function (with respect to x) is:
`y'=m`

This function, `y=mx+b`, represents, graphically, a straight line and the number `m` represents the SLOPE of the line (or if you want the inclination of the line).
As you can see deriving the linear function `y=mx+b` gives you `m`, the slope of the line which is a quite rearcable result, widely used in Calculus!

As an example you can consider the function:
`y=4x+5`
you can derive each factor:
derivative of `4x` is `4`
derivative of `5` is `0`
and then add them together to get:
`y'=4+0=4`

(Remember that the derivative of a constant, `k`, is zero, the derivative of `k*x^n` is `knx^(n-1)` and that `x^0=1` )