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Find all first and second order partial derivatives for each of the following functions

0 votes
Find all first and second order partial derivatives for each of the following functions.

(Find fx(x, y), fy(x, y), fxx(x, y), fyy(x, y), fyx(x, y) and fxy(x, y).)

z = f(x, y) = ln (x^2 + 2xy + y^2 )
asked Oct 18, 2015 in CALCULUS by anonymous

6 Answers

0 votes

(a)

The function is image.

Apply partial derivative on each side with respect to image.

image

image

image

image

image.

answered Oct 19, 2015 by Sammi Mentor
0 votes

(b)

The function is image.

Apply partial derivative on each side with respect to image.

image

image

image

image.

answered Oct 19, 2015 by Sammi Mentor
0 votes

(c)

The function is image.

Find image.

From part (a): image.

Apply partial derivative on each side with respect to image.

image

image

Power rule of partial derivatives: image.

image

image.

answered Oct 19, 2015 by Sammi Mentor
edited Oct 19, 2015 by Sammi
0 votes

(d)

The function is image.

Find .

image

From part (b): .

Apply partial derivative on each side with respect to image.

Power rule of partial derivatives: .

.

answered Oct 19, 2015 by Sammi Mentor
0 votes

(e)

The function is image.

Find image.

From part (b): image.

Apply partial derivative on each side with respect to image.

image

image.

answered Oct 19, 2015 by cameron Mentor
edited Oct 19, 2015 by steve
0 votes

(f)

The function is image.

Find image.

From part (a): image.

Apply partial derivative on each side with respect to image.

image

image

answered Oct 19, 2015 by cameron Mentor

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