Partial Derivatives; Using Partial Derivaties
From Wikiversity
Partial derivatives are when the rates of change of a cross-sectional function gives only part of the picture. Instead of the derivative having a notation of dR/dr the partial derivative notation is ∂R/∂r. This notation is to remind ourselves that there is more than one input variable in the underlying function R.
How to find ∂R/∂r, you will have to treat r as a variable and c as a constant. Make note that r is the variable that is changing and is not held at a constant value.
For Example: R(c,r)= -57.496r² + 4275.432r - 59.247cr + 10,452.325c - 289.638c² so that: Rr = ∂R/∂r = -57.496(2r) + 4275.432(1)- 59.247c(1) + 0 - 0 In essence it would then be: = -114.992r + 4275.432 - 59.247c
We can use partial derivatives to estimate the partial rate of change of revenue with respect to regular sales, or, in general, we find the partial derivative of a multivariable function with respect to one input variabel by treating all other input variables as constants and proceeding to take derivatives as functions of a single input variable. For a two-variable function, a partial rate of change can be visualized graphically as the slope of a line tangent to a cross section.
