Q. 175.0( 1 Vote )

# If yx

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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