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5. continuity and differentiation — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths5. continuity and differentiation1 Mark
MCQ
If $x = {y^{{x^{{y^{{x^{{y^{x = ....\infty }}}}}}}}}}$ , then $y'$ at $x=1$ is
  • ✓
    $1$
  • B
    $2$
  • C
    $5$
  • D
    $7$
✓

Answer

Correct option: A.
$1$
a
$x = {y^{{x^x}}} \Rightarrow \ln x = {x^x}\ln y$   (when $x=1,y=1$)

$\frac{1}{x} = {x^x}\left( {1 + \ln x} \right)\ln y + \frac{{{x^x}}}{y}y'$

$y' = 1$

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