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(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
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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Needed to be solved correclty in 30 Minutes and get the thumbs up please show neat and clean work
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: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.
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
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
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