## Abstract

One of the important problems in mathematics and in its applications in science and engineering is the following: if (1) and the rate of increase of Observe that, for this linear function

*y*=*f*(*x*), find the rate of increase of*y*with respect to*x*. For example, if*y*= 2*x*+ 5, then*y*_{0}= 2*x*_{0}+ 5,*y*_{1}= 2*x*_{1}+ 5, and*y*_{1}—*y*_{0}= 2(*x*_{1}—*>x*_{0}). Thus$$\frac{{{y_1} - {y_0}}}{{{x_1} - {x_0}}} = 2,$$

(1)

*y*with respect to*x*is 2. This example shows that the problem has a simple solution in all cases in which*f*is a linear function. Thus, if*y*=*ax*+*b*, then$$\frac{{{y_1} - {y_0}}}{{{x_1} - {x_0}}} = 2,$$

(2)

*f*, the rate of increase of*y*with respect to*x*is the same, namely*a*, for every*x*_{0}and*x*_{l}.## Keywords

Partial Derivative Linear Transformation Differentiable Function Tangent Plane Chain Rule
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Springer-Verlag New York Inc. 1984