Question

Find dy/dx, x^y × y^x = x+y​

Answer 1

Answer:

x

y

=y

x

.

Taking log on both sides

ylogx=xlogy.

Differentiating both the sides by uv rule

y.

x

1

+logx.

dx

dy

=x.

y

1

dx

dy

+logy

⇒

x

y

−logy=

y

x

.

dx

dy

−logx

dx

dy

⇒

x

y−xlogy

=

dx

dy

(

y

x−ylogx

)

⇒

dx

dy

=

y

x−ylogx

x

y−xlogy

⇒

dx

dy

=

x

y

(

x−ylogx

y−xlogy