Understanding Engineering Mathematics

(vi) 0,

1

3

(vii) 0,− 5 e−^2 (viii) 0,

19

6

√

3

(ix) Doe not exist,−

1
5
5.Answers listed in the orderzx,zy,zz

(i) 2x,4y,6z (ii)

x

d

,

y

d

,

z

d

whered=( 1 −x^2 −y^2 −z^2 )^3 /^2

(iii) yz,xz,xy

(iv) cos(x+yz)−xsin(x+yz),−xzsin(x+yz),−xysin(x+yz)

(v) exy

(

yln(x+y+z)+

1

x+y+z

)

,exy

(

xln(x+y+z)+

1

x+y+z

)

,

exy

x+y+z

6.Answers are given in the orderwxx,wyy,wxy

(i) 2, 2, 0

(ii) 0,

2 x

y^3

,−

1

y^2

(iii) 6x+ 2 y,12y^2 ,2x

(iv)

2 x^2 −y^2

(x^2 +y^2 )^5 /^2

,

2 y^2 −x^2

(x^2 +y^2 )^5 /^2

,

3 xy

(x^2 +y^2 )^5 /^2

(v) y^2 exycos( 3 y^2 ),exy(x^2 cos( 3 y^2 )− 12 xysin( 3 y^2 )−6sin( 3 y^2 )

− 36 y^2 cos( 3 y^2 )),exy(cos( 3 y^2 )+xycos( 3 y^2 )− 6 y^2 sin( 3 y^2 ))

(vi) −

y^2

( 1 +xy)^2

,−

x^2

( 1 +xy)^2

,

1

( 1 +xy)^2

(vii) e−xy( 3 xy^3 − 4 y^2 ),e−xy( 3 x^3 y− 4 x^2 ),e−xy( 3 x^2 y^2 − 7 xy+ 1 )

(viii)

2

√

1 +y

,

3 y^2 + 8 y+ 3 x^2 + 8

4 ( 1 +y)^5 /^2

,−

x

( 1 +y)^3 /^2

(ix) 6xtan−^1

(

x

y

)

+

2 x^4 y+ 6 x^2 y^3

(x^2 +y^2 )^2

,

2 x^4 y

(x^2 +y^2 )^2

,

− 2 x^5 − 4 x^3 y^2

(x^2 +y^2 )^2

,

7.Answers in the orderwxx,wyy,wzz,wxy,wxz,wyz

(i) 2,4,6,0,0,0

(iii) 0, 0, 0,z,y,x

(iv) −2sin(x+yz)−xcos(x+yz),−xz^2 cos(x+yz),−xy^2 cos(x+yz),

−zsin(x+yz)−xzcos(x+yz),

−ysin(x+yz)−xycos(x+yz),−xsin(x+yz)−xyzcos(x+yz)