Find the total differential dw. 5. w = x tan¬ y – 2ªyz

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 92E
Question
The Total Differential
Definition 3.11 Let f be a function of x and y. Suppose f is differentiable
at (r, y). We defined the total differential of f, denoted by df, the
function given by
af(r,y)
df = df (x, y, Ax, Ay) =
af(r, y)
dy
Ar +
Ay.
(3.1)
%3D
Note that df is a function in four variables x, y, Ax and Ay. If z =
f(r, y), we write df = dz. We can write (3.1) by
af
af
df :
- dr +
- dy.
%3D
If z = f(x, y), we have
dz
dz
dz
- dx +
- dy.
dy
Remark 3.12 If f is a function of then variables r1, x2, .., a, (i.e. w :
f(#1, 2, ... , "n)) and f is differentiable at P, the total differential of ƒ is the
function values given by
w%3D
dw
dr2 + · · · +
dw
drn
dw =
dri +
Transcribed Image Text:The Total Differential Definition 3.11 Let f be a function of x and y. Suppose f is differentiable at (r, y). We defined the total differential of f, denoted by df, the function given by af(r,y) df = df (x, y, Ax, Ay) = af(r, y) dy Ar + Ay. (3.1) %3D Note that df is a function in four variables x, y, Ax and Ay. If z = f(r, y), we write df = dz. We can write (3.1) by af af df : - dr + - dy. %3D If z = f(x, y), we have dz dz dz - dx + - dy. dy Remark 3.12 If f is a function of then variables r1, x2, .., a, (i.e. w : f(#1, 2, ... , "n)) and f is differentiable at P, the total differential of ƒ is the function values given by w%3D dw dr2 + · · · + dw drn dw = dri +
Find the total differential dw.
5. w = x tan¬ y – 2ªyz
Transcribed Image Text:Find the total differential dw. 5. w = x tan¬ y – 2ªyz
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