Understanding Engineering Mathematics

(やまだぃちぅ) #1

2.(i)


1

(^0) y
1
3
z
x
(ii)
x
z
− 3 − 1 0 y
1
3
3



  1. (i) 2x,2y (ii)


1
y

,−

x
y^2

(iii) 3x^2 + 2 xy, x^2 + 4 y^3 (iv) −

x
(x^2 +y^2 )^3 /^2

,−

y
(x^2 +y^2 )^3 /^2

(v) yexycos( 3 y^2 ),exy(xcos( 3 y^2 )− 6 ysin( 3 y^2 )) (vi)

y
1 +xy

,

x
1 +xy

(vii) e−xy(y− 3 xy^2 ),e−xy(x− 3 x^2 y) (viii)

2 x

1 +y

,

3 y^2 + 4 y−x^2
2 ( 1 +y)^3 /^2

(ix) 3x^2 tan−^1

(
x
y

)
+

yx^3
x^2 +y^2

,−

x^4
x^2 +y^2


  1. (i) 0, 6 (ii) Does not exist,−


1
4

(iii) 0, 33

(iv) Does not exist,−

2
5


5

(v) 0,e^2 (cos( 12 )−12 sin( 12 ))
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