Question

Anyone know implicit differentiation?

Answer 1

yes what's your question?

Answer 2

leibniz

Answer 3

how do you do \[y ^{2}+x ^{2}\]

Answer 4

oops srry. That equals 2xy

Answer 5

best be equal to something otherwise you cannot assume \(y\) is a function of \(x\)

Answer 6

\[x^2+y^2=2xy\] think of it as
\[x^2+f^2(x)=2xf(x)\] then
\[2x+2f(x)f'(x)=2xf'(x)+2f(x)\] by the chain rule and product rule. easier just to write
\[2x+2yy'=2xy'+2y\] and then solve for \(y'\) by algebra

Answer 7

are we looking for dy/dx or dx/dy?

Answer 8

because if we are looking for dy/dx then = 2x + 2yy'=2(y + xy')
Bring the y' together = 2yy' - 2xy' = 2y- 2x
Factor out y' = y'(2y-2x) = 2y-2x
y' = (2y-2x)/ (2y-2x) =1

if we are looking for dx/dy on the other hand = 2xx' + 2y= 2(x'y + x)
Bring the x' together and factor out the x'
2xx'-2x'y=2x-2y
x'(2x-2y)=2x-2y
x'= (2x-2y)/(2x-2y)= 1

same result but you have to be careful about the dx/dy and dy/dx

Answer 9

THnaks!!!!!!