# Calculas Homework

*label*Mathematics

*timer*Asked: Jun 29th, 2018

*account_balance_wallet*$25

**Question description**

Hello, I need help with this homework. All questions should be answered with all steps shown.

Thank you.

## Tutor Answer

Hi, here are the solutions :). if you have questions, let me know :)

MATH 2400

Homework 4 - Due Friday, June 29

Summer 2018

In these problems you should show all of your work in complete mathematical “sentences”, writing

complete English sentences when you explain your logic. Please always staple your homework and

label it with your section number. Late homework will not be accepted.

1. Verify the conclusion of Clairaut’s Theorem (uxy = u yx) for u = cot(x2 + 2y).

Answer:

uxy = ∂

∂y

∂u

∂x

∂u

∂x

===-

∂

∂x

2(x2+y2)

2(x2+y2)*∂/∂x

(x2 +y2)

2(x2+y2)(2x +∂)

= ∂u

∂x

= -2x

∂ ∂u

∂y ∂x

2

(x2 +y2)

∂

∂y

= -2x(2

-2x

2-1(x2+y2)

= -6x

∂

∂y

2(x2+y2)

∂

∂y

-2x

2(x2+y2)

(x2+y2)*cot(x2+y2)) ∂

∂y

* cot(x2+2y)

cot(x2+y2)

2(x2+y2)

∂ ∂

∂x ∂y

2(x2+y2)

* ∂

∂y

(x2+y2) (-

uxy= -8x

== -2

cot(x2+y2)

- (2)

2(x2+y2)

∂

∂x

= (-2) * (2

-2

2(x2+y2))

2-1 (x2+y2)

* ∂

∂x

(x2+y2))

(x2+y2)

= -6

(x2+y2) (-

(x2+y2) * cot(x2+y2)*

∂

∂x

(x2+y2)

2(x2+y2) *cot(x2+y2)(2x+0)

=-4

=-8x 2(x2+y2...

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