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
In-s [12.5K]
2 years ago
6

Find Dy/dX when x^y×y^x=1​

Mathematics
1 answer:
victus00 [196]2 years ago
7 0

by dy/dx, we'll be assuming that "y" is encapsulating a function, a function in terms of "x".

x^y\cdot y^x=1\implies \stackrel{\textit{\large product rule}}{\stackrel{\textit{chain rule}}{yx^{y-1}(1)}\cdot y^x+x^y\cdot \stackrel{\textit{chain rule}}{xy^{x-1}\cdot \frac{dy}{dx}}}~~ = ~~0 \\\\\\ y^{1+x}x^{y-1}+x^{y+1}y^{x-1}\cdot \cfrac{dy}{dx}=0\implies \cfrac{dy}{dx}=\cfrac{-y^{1+x}x^{y-1}}{x^{y+1}y^{x-1}} \\\\\\ \cfrac{dy}{dx}=-~~ y^{(1+x)-(x-1)}~~x^{(y-1)-(y+1)} \\\\\\ \cfrac{dy}{dx}=-~~ y^2x^{-2}\implies \cfrac{dy}{dx}=\cfrac{-y^2}{x^2}

You might be interested in
HEYOO PEEPSThe angle of a line on a graph is called ______________. One a distance vs. time graph this is also the speed of the
White raven [17]
Length I am pretty sure
3 0
2 years ago
Book $22.50 markup percent 42% what is the markup and retail price.
sertanlavr [38]
I multiplied, I converted the percentage to a decimal .42
Your answer should be 9.45. 
8 0
3 years ago
Read 2 more answers
Line CD passes through points C(3, -5) And D(6, 0). What is the equation of line CD in standard form?
Fynjy0 [20]
Y = mx + b
m = (0 - -5)/(6 - 3) = 5/3
y = 5/3x + b
0 = 5/3(6) + b
b = -10
(y = 5/3x - 10)3
3y = 5x - 30
3y - 5x = -30
5x - 3y = 30
8 0
3 years ago
Read 2 more answers
How many counters would you place in the five frame to show the number
Leviafan [203]
Assuming the five frame is for the number five (5) then place 5 counters in the frame.
7 0
3 years ago
(2x-3)(4-3x) Find the product of the binomials
kobusy [5.1K]
(2X-3)(4-3X)
=8X-6X²-12+9X
=-6X²+17X-12
That's your answer.
7 0
3 years ago
Read 2 more answers
Other questions:
  • Which function transforms the graph of y=x^2 so that it is first shifted down 4 units and is then reflected across the y-axis?
    11·1 answer
  • Graph f (x) = 1.6x-2 +1<br> describe the domain and range<br> describe x- and y- intercepts
    6·1 answer
  • The crazy 80’s baby goes shopping for ingredients at the grocery store. For every 7 carrots that he sees at the store, 2 are rot
    9·2 answers
  • Why did populist party want to have a silver standard instead of a gold standard?
    9·1 answer
  • about 60% of the normal human beings body weight is composed is water. How much of a 125 pound person is water weight?
    15·1 answer
  • The figure shows two parallel lines KL and NO cut by the transversals KO and LN:
    15·2 answers
  • Which one of the following statements expresses a true proportion?
    10·1 answer
  • The math test has 10 multiple choice questions, each with 3 answers. If Betty guesses correctly on the first 3 questions, what i
    6·2 answers
  • F(x) = (2x² – 3)^(-2a? – 9)11
    6·1 answer
  • The ratio of length to width in a rectangle is 3 to 1. If the perimeter of the rectangle is 120 feet, what is the length of the
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!