Given that y^x=x^y, wich of the following expressions equal dy/dx?

E. dy/dx = y (y − x ln y) / (x (x − y ln x))

Step-by-step explanation:

yˣ = xʸ

Take log of both sides.

ln yˣ = ln xʸ

x ln y = y ln x

Implicit derivative (use product rule and chain rule).

x (1/y dy/dx) + ln y (1) = y (1/x) + ln x (dy/dx)

Solve for dy/dx.

x/y dy/dx + ln y = y/x + ln x dy/dx

x² dy/dx + xy ln y = y² + xy ln x dy/dx

(x² − xy ln x) dy/dx = y² − xy ln y

dy/dx = (y² − xy ln y) / (x² − xy ln x)

dy/dx = y (y − x ln y) / (x (x − y ln x))

E

Step-by-step explanation:

x^y = y^x

y lnx = x lny

Differentiation both sides with respect to x

(y' × lnx) + (y/x) = lny + x(1/y)y'

y'lnx + y/x = lny + (x/y)y'

y'[lnx - x/y] = lny - y/x

y'[(ylnx - x)/y] = (xlny - y)/x

y' = [y(xlny - y)] ÷ [x(ylnx - x)]

y' = [y(y- xlny)] ÷ [x(x - ylnx)]

total amount of money that he should pay if he has not used his duty free exemption is $98

step-by-step explanation:

given a united states citizen returning to the states declares the following items at the customs office: 3 shirts at $8.50 each 2 dresses at $27.50 each 1 pair of gold cuff links at $17.50 per pair. we have to find how much he pay

cost of 3 shirts if one cost at $8.50 is

cost of 2 dresses if one cost at $27.50 is  

cost of 1 pair of gold cuff at $17.50

so, total amount of money that he should pay if he has not used his duty free exemption is   $25.5+$55+$17.50=$98

step-by-step explanation:

well if you round, things become much more simple. round 5.95 to 6, 4.25 to 4, and 1.05 to 1. now, add 6+4+1 and that would equal 11. so the items together would equal to about $11.