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CH 1- Partial Derivatives 1. Find all the 1st order partial derivatives of the foll owing function: v = cos(x +2y)-e*- +y f (u,v, p,t) = 8u'r'p-Vv pr* +2u°t +3p* -v x² R(x,y)= y y +1 x+y

CH 1- Partial Derivatives 1. Find all the 1st order partial derivatives of the foll owing function: v = cos(x +2y)-e*- +y f (u,v, p,t) = 8u'r'p-Vv pr* +2u°t +3p* -v x² R(x,y)= y y +1 x+y

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Home Work CH 1- Partial Derivatives 1. Find all the 1st order partial derivati ves of the foll owing function: w = cos(x +2y)-e*r-: + v f (u,v, p,t) = 8u'tp-Vv p't* +2u't+3p* -v y? y +1 x+y R(x,y) =- 2. Determine if f (x, y) = x In (4y)+x+y is increasing or decreasing at (-3,6) if (a) we allow x to vary and hold y fixed. (b) we allow y to vary and hold x fixed. Determine if f (x, y) = x sin() is increasing or decreasing at (-2,) if (a) we allow x to vary and hold y fixed. (b) we allow y to vary and hold x fixed. 3. Verify Clairaut' s Theorem for the given function: A(x, y) = cos + plo Q(s.t) = In (st)-s* sin (6r) + st f (u,w) = sin (uw)+ 4u'w 4. Find all 2nd order derivatives for the given function
Transcribed Image Text:Home Work CH 1- Partial Derivatives 1. Find all the 1st order partial derivati ves of the foll owing function: w = cos(x +2y)-e*r-: + v f (u,v, p,t) = 8u'tp-Vv p't* +2u't+3p* -v y? y +1 x+y R(x,y) =- 2. Determine if f (x, y) = x In (4y)+x+y is increasing or decreasing at (-3,6) if (a) we allow x to vary and hold y fixed. (b) we allow y to vary and hold x fixed. Determine if f (x, y) = x sin() is increasing or decreasing at (-2,) if (a) we allow x to vary and hold y fixed. (b) we allow y to vary and hold x fixed. 3. Verify Clairaut' s Theorem for the given function: A(x, y) = cos + plo Q(s.t) = In (st)-s* sin (6r) + st f (u,w) = sin (uw)+ 4u'w 4. Find all 2nd order derivatives for the given function
g(u,v) =u'v - 2uvv +u° -sin(3v) f(5.1)=s'1 + In(r° -s) h(x,y) =e*s _L 5. Compute the differenti al of each of the following functions: f (x, y) = tan(xy) xy f(x,y, z) = In 6. dw Given the following information use the Chain Rule to determine dt w = x=t +7, y= cos(2t), z = 41 ôz Given the following information use the Chain Rule to determine and ди z =x*y° - 4x x = u'v, y=v- 3u Given the following information use the Chain Rule to determine z, and z, . z = 4y sin (2x) x = 3u – p, y= p²u, u=f +1 Determine formulas for and for the following situation. w = w(x, y, z) x= x(t), y=y(u,v, p), z=z(v,p), v=v(r,u), p= p(t,u) dy for the following equation. dx Compute x'y -3 = sin (xy)
Transcribed Image Text:g(u,v) =u'v - 2uvv +u° -sin(3v) f(5.1)=s'1 + In(r° -s) h(x,y) =e*s _L 5. Compute the differenti al of each of the following functions: f (x, y) = tan(xy) xy f(x,y, z) = In 6. dw Given the following information use the Chain Rule to determine dt w = x=t +7, y= cos(2t), z = 41 ôz Given the following information use the Chain Rule to determine and ди z =x*y° - 4x x = u'v, y=v- 3u Given the following information use the Chain Rule to determine z, and z, . z = 4y sin (2x) x = 3u – p, y= p²u, u=f +1 Determine formulas for and for the following situation. w = w(x, y, z) x= x(t), y=y(u,v, p), z=z(v,p), v=v(r,u), p= p(t,u) dy for the following equation. dx Compute x'y -3 = sin (xy)
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