If f(x, y) = x log y + y log x then fxy = ?
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Answer:
f(x y)=sin(log(x y))=sin(log x +logy)
f(
y
x
)=sin(log x−logy)
f(x y)+f(
y
x
)=sin(log x +logy)+sin(log x−logy)
[∵sin(A+B)+sin(A−B)=2sinAcosB]
=2sin(log x)cos(logy)
∴f(x y)+f(
y
x
)−2sin(log x)cos(logy)=0
f(x y)+f(
y
x
)−2f(x)cos(logy)=0
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