What is the derivative of ##mx+b##?

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## )