Question

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

Answer #1

Find all the second order partial derivatives of the
function
w = x - y / x2 + y

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)

List these six partial derivatives for z = 3 x2 y +
cos (x y) – ex+y
dz/dx dz/dy d2z/dx2 d2z/
dy2 d2z/dxdy d2z/dydx
Evaluate the partial
derivative
dz at the point (2, 3,
30) for the function z = 3 x4 – x y2
dx

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

Find the derivatives dy/dx and d^2y/dx^2, and evaluate them at t
= 2.
x=t^2 ,y = t ln t

find dy/dx
a. (x+y)^4 =4y-9x
b. y= (x +6)^2x
c. y= cos^-1 (3x^2 -5x +1 )

Find all second partial derivatives of the function:
f(x,y) = x2y - 3xy3

Calculate all four second-order partial derivatives for the
function f(x,y)=3+6x2y2 ?

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...

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

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