1. Tardigrade
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  3. Mathematics
  4. Let x= ln x, y=2 ln y, z=3 ln z. Then the value of x1 / x ⋅ y1 / y ⋅ z1 / z is equal to

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Q. Let $x=\ln x, y=2 \ln y, z=3 \ln z$. Then the value of $x^{1 / x} \cdot y^{1 / y} \cdot z^{1 / z}$ is equal to

Continuity and Differentiability

Solution:

$ x ^{1 / x}= e , y ^{1 / y }= e ^{1 / 2}, z ^{1 / z }= e ^{1 / 3}$
$x ^{1 / x } \cdot y ^{1 / y } \cdot z ^{1 / z }= e ^{1+1 / 2+1 / 3}= e ^{11 / 6}$