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\displaystyle \frac{d}{d\lambda}\left( \frac{x^{\lambda}-1}{\log{x}} \right) = \frac{d}{d\lambda}\left( \frac{x^{\lambda}}{\log{x}} \right) = \frac{1}{\log{x}}\frac{d}{d \lambda}\left x^{ \lambda}
\displaystyle \frac{d}{d \lambda}\left x^{ \lambda} = x^{\lambda}\log{x}
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\displaystyle f\left( \frac 12\right) \equal{} 0
\displaystyle \[ \int^1_0 \left( f'(x) \right)^2 dx \geq 12 \left( \int^1_0 f(x) dx \right)^2.\]
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\displaystyle f\left( \frac 12\right) \equal{} 0
\displaystyle \[ \int^1_0 \left( f'(x) \right)^2 dx \geq 12 \left( \int^1_0 f(x) dx \right)^2.\]
\displaystyle f\left( \frac 12\right) \equal{} 0
\displaystyle \[ \int^1_0 \left( f'(x) \right)^2 dx \geq 12 \left( \int^1_0 f(x) dx \right)^2.\]
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