Zahriatu Aida 2502131346
Diskusi 2 – Turunan Parsial
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Tentukan turunan parsial dari fungsi-fungsi di bawah ini
1. z = ln √
=
(
)
√(
=
=
√(
)
√(
)
)
(
)(
(
)
)
)
√(
=
2. z = 36 – x2 – y2
= fx(x,y) = -2x
= fy(x,y) = -2y
fxx(x,y) = -2
fyy(x,y) = -2
fxy(x,y) = 0
3. z = 3 -
√
(
)
=(
=-
√
(
(
(
(
))
(
(
))
)
))
MATH6162 - Mathematics
4. z = xy2 – 2x2 + 3y3
= fx(x,y)
= y2 – 4x
= fy(x,y)
= 2xy + 6y
= fxx(x,y) = -4
= fyy(x,y) = 2x + 6
5. z = arc tan
=
=
y
( )
( )
6. f(x,y,z) = xy – yz + xz
(
)
(
)
=x–z
(
)
=x–y
=y+z
=
=
=
7. f(x,y,z) = √
(
)
=(
= (
=
√(
)
)
. 2x
)
MATH6162 - Mathematics
(
)
= (
=
(
)
= (
)
. 2z
)
√(
=
. 2y
)
√(
=
)
√(
)
√(
)
.
√(
)
√(
)
√(
)
=
=
.
=
=
)
√(
.
=
8. f(x,y,z) = sin (xy) – 2exy
(
)
= x cos (xy) – 2x. exy
(
)
= y cos (xy) – 2y. exy
=
(
)
(
)
9. f(x,y,z) = arc sin ( )
(
(
(
)
)
)
=
√
(
)
√
(
)
√
(
)
=
=
xy
MATH6162 - Mathematics
.√
=
√
(
)
√
(
)
√
(
)
( ) .
=
=
.√
( ) .
.√
( ) .
=
=
=
MATH6162 - Mathematics