Q. 123.9( 56 Votes )

# Find dy/dx of the functions.

x^{y} + y^{x} = 1

Answer :

Given: x^{y} + y^{x} = 1

Let y= x^{y} + y^{x} = 1

Let u = x^{y} and v = y^{x}

Then, ⇒ u + v = 1

For, u = x^{y}

Taking log on both sides, we get

Log u =log x^{y}

⇒log u = y.log(x)

Now, differentiate both sides with respect to x

For, v = y^{x}

Taking log on both sides, we get

Log v =log y^{x}

⇒log v = x.log(y)

Now, differentiate both sides with respect to x

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