1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Klio2033 [76]
3 years ago
12

Find the second partial derivatives of the following functions

Mathematics
1 answer:
artcher [175]3 years ago
6 0

(a) <em>z</em> = 3<em>x</em> ² - 4<em>xy</em> + 15<em>y</em> ²

has first-order partial derivatives

∂<em>z</em>/∂<em>x</em> = 6<em>x</em> - 4<em>y</em>

∂<em>z</em>/∂<em>y</em> = -4<em>x</em> + 30<em>y</em>

and thus second-order partial derivatives

∂²<em>z</em>/∂<em>x</em> ² = 6

∂²<em>z</em>/∂<em>x</em>∂<em>y</em> = -4

∂²<em>z</em>/∂<em>y</em>∂<em>x</em> = -4

∂²<em>z</em>/∂<em>y</em> ² = 30

where ∂²<em>z</em>/∂<em>x</em>∂<em>y</em> = ∂/∂<em>x</em> [∂<em>z</em>/∂<em>y</em>] and ∂²<em>z</em>/∂<em>y</em>∂<em>x</em> = ∂/∂<em>y</em> [∂<em>z</em>/∂<em>x</em>].

(b) <em>z</em> = 4<em>x</em> <em>eʸ</em>

∂<em>z</em>/∂<em>x</em> = 4<em>eʸ</em>

∂<em>z</em>/∂<em>y</em> = 4<em>x</em> <em>eʸ</em>

∂²<em>z</em>/∂<em>x</em> ² = 0

∂²<em>z</em>/∂<em>x</em>∂<em>y</em> = 4<em>eʸ</em>

∂²<em>z</em>/∂<em>y</em>∂<em>x</em> = 4<em>eʸ</em>

∂²<em>z</em>/∂<em>y</em> ² = 4<em>x</em> <em>eʸ</em>

<em />

(c) <em>z</em> = 6<em>x</em> ln(<em>y</em>)

∂<em>z</em>/∂<em>x</em> = 6 ln(<em>y</em>)

∂<em>z</em>/∂<em>y</em> = 6<em>x</em>/<em>y</em>

∂²<em>z</em>/∂<em>x</em> ² = 0

∂²<em>z</em>/∂<em>x</em>∂<em>y</em> = 6/<em>y</em>

∂²<em>z</em>/∂<em>y</em>∂<em>x</em> = 6/<em>y</em>

∂²<em>z</em>/∂<em>y</em> ² = -6<em>x</em>/<em>y</em> ²

You might be interested in
What is 2 x 9 x 18 x 28 x 46 x 58, its a hard question
Yuliya22 [10]
2x9 is 18x18 is 324 x28 is 9072 x 46 is 417,312 so the x 58 the answer is 24,204,096
8 0
3 years ago
Read 2 more answers
There was a seller of horses, who sold all his horses to three people. To the first man he sold half of all his horses and a hal
Nata [24]

Answer:

7

Step-by-step explanation:

3RD MAN: 1

2ND MAN: 2

1ST MAN: 4

3rd Man = 1/2+1/2 = 1

2nd Man = 1+1 = 2

1st Man = 2*2 = 4

7 0
3 years ago
Read 2 more answers
Urgent helps bxjdidjdjjfjdhhdhdh
MatroZZZ [7]

Answer:

l=40

Step-by-step explanation:

The area is calculated as

A = wl

1200=30l

1200/30=l

40=l

5 0
3 years ago
PLEASE HELP! NO ONE HAS BEEN HELPING WITH MY QUESTIONS SO IT WOULD MEAN A LOT IF YOU DID!
kvv77 [185]

Answer:

80 m²

Step-by-step explanation:

The area (A) of a trapezoid is calculated as

A = \frac{1}{2} h (a + b)

where h is the perpendicular height between bases and a, b are the bases

Here h = 8, a = 14 and b = 6, thus

A = \frac{1}{2} × 8 × (14 + 6) = 4 × 20 = 80 m²

3 0
3 years ago
Noah says that 9X minus 2X plus 4X is equivalent to 3X because the subtraction sign tells us to subtract everything that comes a
lesantik [10]

Answer:

False

Step-by-step explanation:

It is given that Noah thinks :

9x - 2x + 4x = 3x   as the subtraction sign after 9x tells us to subtract everything that comes after 9x.

This is wrong as according to the BODMAS rule, we have to do the addition operation first and then followed by subtraction operation.

That is

⇒ 9x - 2x + 4x

⇒ (9x -2x)+ 4x

⇒ 7x + 4x

⇒ 11x

Therefore the answer to the equation is 11x and not 3x.

8 0
3 years ago
Other questions:
  • 34.14% out of 90 students is how many students?
    11·2 answers
  • Suppose f(x)=x^2.Find the graph of f(x+3)
    6·2 answers
  • If Company X has 1600 employees and 80% of those employees have attended the warehouse training course how many employees have y
    12·1 answer
  • Which property of equality would be used to isolate the variable a in this equation?. a – 4 = 12. A. addition property of equali
    12·2 answers
  • Janelle says that lines l and m are skew lines. is janelle correct? yes, because the lines are not parallel. yes, because the li
    14·2 answers
  • Is 563 divisibly by 4
    13·2 answers
  • Which equation matches the graph
    7·1 answer
  • In a class of pupils, 11 play the flute and piano.
    9·1 answer
  • Plz help! will give brainliest!!!
    5·1 answer
  • Martha has 2 apples if she buys 2 more how much does she have?
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!