Answer :

To find:

Taking given equation y^{x} + x^{y} + x^{x} = a^{b}

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

∴ Our given equation becomes u + v + w = a^{b}

…(A)

Now, u = y^{x}

Taking log on both the sides, we get

log u = x logy

Differentiating with respect to x, we get

…(i) [replacing u by y^{x}]

Now, v = x^{y}

Taking log on both the sides, we get

log v = y logx

Differentiating with respect to x, we get

…(ii) [replacing v by x^{y}]

Also, w = x^{x}

Taking log on both the sides, we get

log w = x logx

Differentiating with respect to x, we get

…(iii) [replacing w by x^{x}]

Substituting the value of eq. (i), (ii) and (iii) in eq. (A), we get

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