(a) Find the partial derivative of f with respect to x. fx(X, y) = (b) Find the partial derivative of f with respect to y. fy(x, y) =
(a) Find the partial derivative of f with respect to x. fx(X, y) = (b) Find the partial derivative of f with respect to y. fy(x, y) =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Needed to be solved correclty in 30 Minutes and get the thumbs up please show neat and clean work
Transcribed Image Text:Problem 1: a, b
The directional derivative, which is a rate of change of a multivariable function in any direction.
Partial derivatives turn out to be directional derivatives along the coordinate axes.
Okasato us fotolia.com
f(x,y) = y+
The derivative of f(x,y) at the point (x,y) in the direction of the unit vector = (a, b) is:
Dif (x, y) = lim fa+ah, y+bh)–f(x, y)
h-0
Select Surface 3, the function
ху
if (x, y) + (0, 0)
f(x, у)
x2
+ y2
if (x, y) = (0, 0).
under the Explore & Test section of the Explore It.
Transcribed Image Text:DIRECTIONAL DERIVATIVES
Surface 1
Surface 2
Surface 3
Select one of the three points,
then specify the direction of
the unit vector by dragging the
yellow arrow or typing in a
vector.
1. When moving through the point
(-1, 0.75), in which of the following
directions does the function
decrease? Check all that apply.
O West
O Southwest
O South
O Southeast
D7f (0 ,0) =
ư
(0,0) O(-1 ,0.75) O(0.01 ,0.05)
To rotate grid, click and drag
Rotate view 360° O Display direction plane
=(0.707 ,0.707 )
Ild||
xy
if (x, y) # (0, 0)
f (x, y) =
x2+y?
if (x, y) = (0,0)
d = (0.5
0.5
SUBMIT
South
(a) Find the partial derivative of f with respect to x.
fx(X, y) =
(b) Find the partial derivative of f with respect to y.
f,(x, v) =
West
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
