Answer :
Given that
Differentiating with respect to itself, we get
Simplifying, we get
x dx + y dy = x dy – y dx
or
dx(x + y)= dy(x-y)
Hence,
OR
Given that xy-yx=ab
Let u= xy and v= yx, then we get
u-v= ab
Differentiating with respect to x, we get
(Since ab is constant) …. (1)
u= xy
Taking log both sides
Differentiating with respect to x, we get
⇒
Hence, ….. (2)
v= yx
Taking log both sides
Differentiating with respect to x, we get
⇒
Hence, ……(3)
Substituting (2) and (3) in (1), we get
Simplifying, we get
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