Select Surface 1, the function f(x, y) = x + xy + y, under the Explore & Test section of the Explore It. (a) Find the partial derivative of f with respect to x. 1,(x, y) = (b) Find the partial derivative of f with respect to y. (c) Set the direction to point south, which is along the positive x-axis in this case. Select the point (1, -1). What is the directional derivative? (d) Evaluate , at the point (1, -1) and compare with your answer to part (c). (1, -1) = (e) Set the direction to point east, which is along the positive y-axis in this case. Select the point (1, -1). What is the directional derivative? (f) Evaluate fy at the point (1, -1) and compare with your answer to part (e). y(1, -1) =
Select Surface 1, the function f(x, y) = x + xy + y, under the Explore & Test section of the Explore It. (a) Find the partial derivative of f with respect to x. 1,(x, y) = (b) Find the partial derivative of f with respect to y. (c) Set the direction to point south, which is along the positive x-axis in this case. Select the point (1, -1). What is the directional derivative? (d) Evaluate , at the point (1, -1) and compare with your answer to part (c). (1, -1) = (e) Set the direction to point east, which is along the positive y-axis in this case. Select the point (1, -1). What is the directional derivative? (f) Evaluate fy at the point (1, -1) and compare with your answer to part (e). y(1, -1) =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text: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.
Okasatootoia.com
f(x,y) = y*
The derivative of f(x.y) at the point (x.y) in the direction of the unit vector i= (a, b) is:
f(x+ah, y+bh)-f(x, y)
Df (x, y) = lim
Transcribed Image Text:Select Surface 1, the function f(x, y) = x + xy + y, under the Explore & Test section of the Explore It.
(a) Find the partial derivative of f with respect to x.
1,(x, y) =
(b) Find the partial derivative of f with respect to y.
y(x, Y) =
(c) Set the direction to point south, which is along the positive x-axis in this case. Select the point (1, -1). What is the directional derivative?
(d) Evaluate , at the point (1, -1) and compare with your answer to part (c).
(1, -1) =
(e) Set the direction to point east, which is along the positive y-axis in this case. Select the point (1, -1). What is the directional derivative?
() Evaluate fy at the point (1, -1) and compare with your answer to part (e).
(1, -1) =
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