Suppose that z is a difierentiable function of x and y with ∂ z ∂ x ( 1 , 2 ) = 4 and ∂ z ∂ y ( 1 , 2 ) = 2 If x = x ( t ) and y = y ( t ) are differentiable function of t with x ( 0 ) = 1 , y ( 0 ) = 2 , x ' ( 0 ) = − 1 2 , and (under composition ) z ' ( 0 ) = 2 , find y'(0) .
Suppose that z is a difierentiable function of x and y with ∂ z ∂ x ( 1 , 2 ) = 4 and ∂ z ∂ y ( 1 , 2 ) = 2 If x = x ( t ) and y = y ( t ) are differentiable function of t with x ( 0 ) = 1 , y ( 0 ) = 2 , x ' ( 0 ) = − 1 2 , and (under composition ) z ' ( 0 ) = 2 , find y'(0) .
Suppose that z is a difierentiable function of x and y with
∂
z
∂
x
(
1
,
2
)
=
4
and
∂
z
∂
y
(
1
,
2
)
=
2
If
x
=
x
(
t
)
and
y
=
y
(
t
)
are differentiable function of t with
x
(
0
)
=
1
,
y
(
0
)
=
2
,
x
'
(
0
)
=
−
1
2
,
and
(under composition )
z
'
(
0
)
=
2
,
find
y'(0)
.
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