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# )

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Answer 2

Elijah Abram

The derivative of mx + b with respect to x is simply m, as the derivative of a constant (b) with respect to x is 0, and the derivative of mx with respect to x is m.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.