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Find the Partial Derivatives of t 1) f(x,y) = 2x - 3y -4 2) S(x, y) = (x' -1Xy+ 2) 3) f(x, y) = (xy-1}

Find the Partial Derivatives of t 1) f(x,y) = 2x - 3y -4 2) S(x, y) = (x' -1Xy+ 2) 3) f(x, y) = (xy-1}

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 70EQ
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11:-1 37 - 51.pdf > Exercises Find the Partial Derivatives of the functions with respect to each variable 1) f(x,y) = 2x - 3y-4 Ans. f, 4x, f, =-3 2) f(x, y) = (x* -1)Xy+ 2) Ans. f,= 2x(y+ 2), f, = x' -1 3) f(x, y) = (xy-1) Ans. f, = 2y(xy-1), f, 2x(xy-1) 4) S(x, y) = Vx² + y° Ans. f,=T+ys Ja +y* 42 Mathematics Second Year Electrical & Electronic Engineering Department Dr. Atheer Alaa Sabri -1 f%3D (x+y) -1 f(x, y) = x+y 5) Ans. f, = (r+ y} -x' -1 - y' -1 (ху— 1)? x+y 6) f(x, y)=- xy -1 Ans. f. = (xy-1) 7) f(x, y) = e*y+1) Ans. f. =e*y+1), f. = e*+y+1) 1 f, x+ y 1 8) f(x, y) = In(x+ y) Ans. f, = x+y 9) S(x, y) = sin'(x-3y) Ans. f, =2 sin(x-3y)cos(x-3y), f, =-6 sin(x-3y) cos(x-3y) 10) f(x, y) =x' Ans. f, = yx, f, = x' In(x) 11) f(x.y) =Jg()dt, Ans. f, =-g(x), f, = g(y) (g continuous for all t) 12) f(x, y,z) = 1+xy- 22 Ans. f,=y', f, = 2.xy, f, =-4z 13) f(x, y,z) =x-Vy? +z Ans. f, =1, f, =-yly* +z')"², S. =--(y* +=')"? %3D II
Transcribed Image Text:11:-1 37 - 51.pdf > Exercises Find the Partial Derivatives of the functions with respect to each variable 1) f(x,y) = 2x - 3y-4 Ans. f, 4x, f, =-3 2) f(x, y) = (x* -1)Xy+ 2) Ans. f,= 2x(y+ 2), f, = x' -1 3) f(x, y) = (xy-1) Ans. f, = 2y(xy-1), f, 2x(xy-1) 4) S(x, y) = Vx² + y° Ans. f,=T+ys Ja +y* 42 Mathematics Second Year Electrical & Electronic Engineering Department Dr. Atheer Alaa Sabri -1 f%3D (x+y) -1 f(x, y) = x+y 5) Ans. f, = (r+ y} -x' -1 - y' -1 (ху— 1)? x+y 6) f(x, y)=- xy -1 Ans. f. = (xy-1) 7) f(x, y) = e*y+1) Ans. f. =e*y+1), f. = e*+y+1) 1 f, x+ y 1 8) f(x, y) = In(x+ y) Ans. f, = x+y 9) S(x, y) = sin'(x-3y) Ans. f, =2 sin(x-3y)cos(x-3y), f, =-6 sin(x-3y) cos(x-3y) 10) f(x, y) =x' Ans. f, = yx, f, = x' In(x) 11) f(x.y) =Jg()dt, Ans. f, =-g(x), f, = g(y) (g continuous for all t) 12) f(x, y,z) = 1+xy- 22 Ans. f,=y', f, = 2.xy, f, =-4z 13) f(x, y,z) =x-Vy? +z Ans. f, =1, f, =-yly* +z')"², S. =--(y* +=')"? %3D II
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