Question

List these six partial derivatives for z = 3 x^{2} y +
cos (x y) – e^{x+y}

dz/dx dz/dy d^{2}z/dx^{2} d^{2}z/
dy^{2} d^{2}z/dxdy d^{2}z/dydx

- Evaluate the partial
derivative
dz at the point (2, 3,
30) for the function z = 3 x
^{4}– x y^{2}

dx

Answer #1

1)
If z=Ln(x2+y2 ) , x=e-1
,y=et the total derivative dz/dt will
become--------------
Select one:
A. dz/dt=2x/x2+ y2 . (-e-t) -
2x/(x2+ y2 ). et
B. dz/dt=2x/x2+ y2 .
(-e-t)+2x/(x2+ y2 ).
e-t
C. dz/dt=2x/x2+ y2 .
(-e-t)+2x/(x2+ y2 ).
et
D. dz/dt=2x/x2+ y2 .
(e-t)+2x/(x2+ y2 ).
et
2)
The second order partial derivative with respect to x of
f(x,y)=cos(x)+xyexy+xsin(y) is-------------
Select one:
A. ∂/∂x(∂f/∂x) = 2y2exy +
xy3exy
B. ∂/∂x(∂f/∂x) = −cos(x) + 2y2exy +
xy3exy + sin(y)...

Find all the second-order partial derivatives of the following
function. w=(3x-4y)/(3x^2+y)
d^2w/dx^2
d^2w/dy^2
d^2w/dydx
d^2w/dxdy

find dx/dx and dz/dy
z^3 y^4 - x^2 cos(2y-4z)=4z

(part a) Assume that x and y are positive functions of t. If x2
+ y2 = 100 and dy/dt = 4, find dx/dt when y = 6.
(part b) Suppose x, y, and z are
positive functions of t. If z2 = x2
+ y2, dx/dt = 2, and dy/dt = 3, find dz/dt when x = 5
and y = 12.

compute partial derivatives df/dx and df/dy, and all second
derivatives of the function:
f(x,y) = [4xy(x^2 - y^2)] / (x^2 + y^2)

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=

Find the first- and second-order partial derivatives for the
following function. z = f (x, y) = (ex +1)ln y.

Evaluate ∮C(x^3+xy)dx+(cos(y)+x2)dy∮C(x^3+xy)dx+(cos(y)+x^2)dy
where C is the positively oriented boundary of the region bounded
by C:0≤x^2+y^2≤16, x≥0,y≥0C:0≤x^2+y^2≤16,x≥0,y≥0

D is the region bounded by:
y = x2, z = 1 − y, z = 0
(not necessarily in the first octant)
Sketch the domain D.
Then, integrate f (x, y, z) over the domain in 6 ways: orderings of
dx, dy, dz.

Evaluate double integral Z 2 0 Z 1 y/2 cos(x^2 )dx dy
(integral from 0 to 2)(integral from y/2 to 1) for cos(x^2) dx
dy

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