Question

If f(x, y) = x log y + y log x then fxy = ?​

Answer 1

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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