Question

find the follwing du/dx u=X log (xy) where x²-xy+y²=a²​

Answer 1

Answer:

Given expression is,

log(x.y)=x

2

+y

2

∴logx+logy=x

2

+y

2

Differentiate both sides w.r.t. x, we get,

x

1

+

y

1

dx

dy

=2x+2y

dx

dy

∴

x

1

−2x=2y

dx

dy

−

y

1

dx

dy

∴(2y−

y

1

)

dx

dy

=

x

1

−2x

∴(

y

2y

2

−1

)

dx

dy

=

x

1−2x

2

∴

dx

dy

=(

2y

2

−1

y

)(

x

1−2x

2

)

∴

dx

dy

=

x(2y

2

−1)

y(1−2x

2

)