Question

Please find ALL second partial derivatives of f: fx, fy, fz, fxx, fyy, fzz, fxy, fxz, and fyz

For ?(?, ?, ?) = (?^?)(?^?)(?^?)

THANK YOU

Answer #1

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

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...

(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=

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.

. For the function x,y=xarctan(xy) , compute
fx , fy ,
fxx , fyy , and
fxy

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.

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

fxx, fxy, fyx, and fyy
f(x, y) = y (ln x)

Find fxx, fxy, fyy when f(x, y) = xe^(x^2−xy+y^2)

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