Page 176 - ADVANCED MATH F.5

Form Five Form Five

f ∂ f ∂
2
2
5. (a) = 3yx + 2 2y x , = x + 3 2x y
x ∂ y ∂
f ∂ f ∂
(b) = 2x + 3, y = 3x
FOR ONLINE READING ONLY
x ∂ y ∂
f ∂ f ∂
3
3
4
2
2
3
(c) = 4x y + 16xy + 5, = 3x y + 8x + 4y
x ∂ y ∂
f ∂ 2x y 2 f ∂ x 2 2y
(d) = − , = − +
x ∂ y x 2 y ∂ y 2 x
∂ 2 z
6. (a) = − x 2 sin(x − 2 ) 4 cos(y + x x − 2 ) 2sin(y + x − 2 )y
x ∂ 2
∂ 2 z
(b) = − 4x 2 sin(x − 2 )y
y ∂ 2

∂ 2 z
(c) = − 4 cos(x x − 2 ) 2y + x 2 sin(x − 2 )y
xy
∂∂
∂ 2 z
(d) = − 4 cos(x x − 2 ) 2y + x 2 sin(x − 2 )y
∂∂
yx

∂ 2 z x ∂ 2 z 2x y − 3 4xy 3
7. x ∂ 2 = − 3 , y ∂ 2 = 3
2
( y − 2 x 2 ) 2 ( 2 y − 4 yx 2 ) 2

∂ 2 z ∂ 2 z
8. = − 0.71 9. = 9 –6
x ∂ 2 y ∂ 2

∂ T π ∂ T π l
10. (a) = (b) = −
l ∂ gl g ∂ g g

170
Mathematics for Advanced Secondary Schools

30/06/2024 18:02:44
ADVANCED MATH F.5 TG CHAPTERS.indd 170 30/06/2024 18:02:44
ADVANCED MATH F.5 TG CHAPTERS.indd 170