Question

Find dw/dt using the appropriate chain rule for w=x^2+y^2+z^2 where x=8tsin(s), y=8tcos(s) and z=5st^2

Answer #1

Let w(x,y,z) = x^2+y^2+z^2 where x=sin(8t), y=cos(8t) , z=
e^t
Calculate dw/dt by first finding dx/dt, dy/dt, and dz/dt and using
the chain rule
dx/dt =
dy/dt=
dz/dt=
now using the chain rule calculate
dw/dt 0=

Use the Chain Rule to find dw/dt.
w = ln
x2 + y2 + z2
, x = 9 sin(t), y
= 4 cos(t), z = 5 tan(t)
dw
dt
=

1.express dw/dt as a function of t, both by using the Chain Rule
and by expressing w in terms of t and differentiating directly with
respect to t. Then evaluate dw/dt at the given value of t.
a)w= -6x^2-10x^2 , x=cos t,y=sint, t=pi/4
b)w=4x^2y-4y^2x, x=cost y=sint, --> express n terms of t
2.Find the linearization L(x,y) of the function (x,y)=e^x
cos(9y) at points (0,0) and (0,pi/2)

Let w = (x 2 -z)/ y4 ,
x = t3+7,
y = cos(2t),
z = 4t.
Use the Chain Rule to express dw/ dt in terms of t. Then
evaluate dw/ dt at t = π/ 2

Consider the function w = x^(2) + y^(2) + z^(2) with x =
tsin(s), y = tcos(s), and z = st^(2)
(a) Find ∂w/∂s and ∂w/∂t by using the appropriate Chain
Rule.
(b) Find ∂w/∂s and ∂w/∂t by first substituting and writing w as
a function of s and t
before differentiating.

use the Chain Rule to find ∂w/∂s for w=e^xcos(y) where
x=s^2sin(t) and y=s/t

Use the Chain Rule to find dz/dt. (Enter your
answer only in terms of t.)
z=sqrt(1+x^2+y^2), x=ln(t), y=cos(t)
dz/dt=

it is known that W=x2y+y+xz where x=cos A, y=sin A,
and z=A2. find DW/DA and calculate the value of
A=1/3

Use the Chain Rule to find dz/dt. (Enter your answer only in
terms of t.) z = sin(x + 7y), x = 8t^2, y = 3/t

Use the Chain Rule to find ∂z/∂s and ∂z/∂t.
3. z=x/y, x=se^t, y=1+se^-t
4. z=e^rcos θ, r=st, θ=√s^2+t^2

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