Question

(1 point)

Find all the first and second order partial derivatives of f(x,y)=7sin(2x+y)−2cos(x−y)

A. ∂f∂x=fx=∂f∂x=fx=

B. ∂f∂y=fy=∂f∂y=fy=

C. ∂2f∂x2=fxx=∂2f∂x2=fxx=

D. ∂2f∂y2=fyy=∂2f∂y2=fyy=

E. ∂2f∂x∂y=fyx=∂2f∂x∂y=fyx=

F. ∂2f∂y∂x=fxy=∂2f∂y∂x=fxy=

Answer #1

part 1)
Find the partial derivatives of the function
f(x,y)=xsin(7x^6y):
fx(x,y)=
fy(x,y)=
part 2)
Find the partial derivatives of the function
f(x,y)=x^6y^6/x^2+y^2
fx(x,y)=
fy(x,y)=
part 3)
Find all first- and second-order partial derivatives of the
function f(x,y)=2x^2y^2−2x^2+5y
fx(x,y)=
fy(x,y)=
fxx(x,y)=
fxy(x,y)=
fyy(x,y)=
part 4)
Find all first- and second-order partial derivatives of the
function f(x,y)=9ye^(3x)
fx(x,y)=
fy(x,y)=
fxx(x,y)=
fxy(x,y)=
fyy(x,y)=
part 5)
For the function given below, find the numbers (x,y) such that
fx(x,y)=0 and fy(x,y)=0
f(x,y)=6x^2+23y^2+23xy+4x−2
Answer: x= and...

Find all second partial derivatives of f : ?(?, ?, ?) =
?^??^??^?
fx=
fy=
fz=
fxx=
fyy=
fzz=
fxy=
fxz=
fyz=

Please find ALL second partial derivatives of f: fx, fy, fz,
fxx, fyy, fzz, fxy, fxz, and fyz
For ?(?, ?, ?) = (?^?)(?^?)(?^?)
THANK YOU

Let f(x, y) = 2x^3y^2 + 3xy^3 4x^3 y. Find
(a) fx
(c) fxx
(b) fy
(d) fyy
(e) fxy
(f) fyx

Suppose that f is a twice differentiable function and that
its second partial derivatives are continuous. Let h(t) =
f (x(t), y(t)) where x = 2e^ t and y = 2t. Suppose that
fx(2, 0) = 1, fy(2, 0) = 3, fxx(2, 0) = 4, fyy(2, 0) = 1, and
fxy(2, 0) = 4. Find d ^2h/ dt ^2 when t = 0.

Suppose that f is a twice differentiable function and that
its second partial derivatives are continuous. Let h(t) =
f (x(t), y(t)) where x = 3e ^t and y = 2t. Suppose that
fx(3, 0) = 2, fy(3, 0) = 1, fxx(3, 0) = 3, fyy(3, 0) = 2, and
fxy(3, 0) = 1. Find d 2h dt 2 when t = 0.

Suppose that the function f(x, y) has continuous partial
derivatives fxx, fyy, and fxy at all points (x,y) near a critical
points (a, b). Let D(x,y) = fxx(x, y)fyy(x,y) – (fxy(x,y))2 and
suppose that D(a,b) > 0.
(a) Show that fxx(a,b) < 0 if and only if fyy(a,b) <
0.
(b) Show that fxx(a,b) > 0 if and only if fyy(a,b) >
0.

You are given that the function f(x,y)=8x2+y2+2x2y+3 has first
partials fx(x,y)=16x+4xy and fy(x,y)=2y+2x2, and has second
partials fxx(x,y)=16+4y, fxy(x,y)=4x and fyy(x,y)=2. Consider the
point (0,0). Which one of the following statements is true?
A. (0,0) is not a critical point of f(x,y).
B. f(x,y) has a saddle point at (0,0).
C. f(x,y) has a local maximum at (0,0).
D. f(x,y) has a local minimum at (0,0).
E. The second derivative test provides no information about the
behaviour of f(x,y) at...

Given w=f(x,y,z)
List all of the second and third derivatives. How many unique
second derivatives? How many unique third derivatives?
Example: If z=f(x,y) , then z has 3 unique derivatives.
fxx, fxy. fyy

Compute all second order partial derivatives of f(x, y) = x^4 −
2x ^3 y^2

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