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Engineering Mathematics Miscellaneous

Engineering Mathematics

  1. Let f = yx. What is
    2f
    at x = 2 , y = 1 ?
    ∂x∂y

    1. 0
    2. ln 2
    3. 1
    4. 1
      ln 2

Correct Option: C

Given f = yx
⇒ ln f = x ln y

1
∂f
=
x
f∂yy

∂f
=
x
.yx
∂yy

Now , ln
∂f
= ln
x
+ x ln y
∂yy

1
2f
=
y
.
1
ln y
∂f / ∂y∂x∂yxy

2f
=
1
+ ln y
x
.yx
∂x∂yxy

=
1
  0 × 2.1 = 1
2



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