Q. 175.0( 1 Vote )

If yx

Answer :

To find:


Taking given equation yx + xy + xx = ab


Let yx = u, xy = v and xx = w


Our given equation becomes u + v + w = ab


…(A)


Now, u = yx


Taking log on both the sides, we get


log u = x logy


Differentiating with respect to x, we get





…(i) [replacing u by yx]


Now, v = xy


Taking log on both the sides, we get


log v = y logx


Differentiating with respect to x, we get





…(ii) [replacing v by xy]


Also, w = xx


Taking log on both the sides, we get


log w = x logx


Differentiating with respect to x, we get





…(iii) [replacing w by xx]


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







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