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,...
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
Consider the function w = x^(2) + y^(2) + z^(2) with x =
tsin(s), y =...
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.
For the function w=f(x,y) , x=g(u,v) , and
y=h(u,v). Use the Chain Rule to
Find...
For the function w=f(x,y) , x=g(u,v) , and
y=h(u,v). Use the Chain Rule to
Find ∂w/∂u and
∂w/∂v when u=2 and v=3 if
g(2,3)=4, h(2,3)=-2,
gu(2,3)=-5,
gv(2,3)=-1 ,
hu(2,3)=3,
hv(2,3)=-5,
fx(4,-2)=-4, and
fy(4,-2)=7
∂w/∂u=
∂w/∂v =
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,...
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 the indicated partial
derivatives.
w = xy + yz +...
Use the Chain Rule to find the indicated partial
derivatives.
w = xy + yz + zx, x = r
cos(θ), y = r
sin(θ), z = rθ;
∂w
∂r
,
∂w
∂θ
when r = 4, θ =
π
2
∂w
∂r
=
∂w
∂θ
=
Use the Chain Rule to find the indicated partial derivatives. u
=sqrt( r^2 + s^2) ,...
Use the Chain Rule to find the indicated partial derivatives. u
=sqrt( r^2 + s^2) , r = y + x cos(t), s = x + y sin(t)
∂u ∂x , ∂u ∂y , ∂u ∂t when x = 1, y = 4, t = 0