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Chapter 12: Q. 2 (page 952)

What is the definition of the directional derivative for a function of three variables, f(x,y,z) ? Be sure to include the words "unit vector" in your definition.

Short Answer

Expert verified

Going to assume that limit exists isDufx0,y0,z0=Limh鈫�0fx0+a路h,y0+b路h,z0+c路h-fx0,y0,z0h

Step by step solution

01

Unit vector.

A vector could be a quantity that has both a magnitude and a directionrelated to it.
A unit vector could be a vector with a magnitude of1
It's alsoobserved as a Direction Vector.

02

Directional Derivative 

Directional Derivative of a function of three variables:

Letf(x,y,z)be a function of two variables defined on an open set containing the point x0,y0,z0, and let u=(a,b,c)be a unit vector.

The directional derivative with infat (xo,yo,zo)in the direction of u, denoted by

localid="1650479588198" Duf(x0,y0,zo), is given by;

Dufx0,y0,z0=Limh鈫�0fx0+a路h,y0+b路h,z0+c路h-fx0,y0,z0h

Provided that a limit existed

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