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$$\frac{\partial \mathcal{L}}{\partial \eta_1}= -\sum_{i=1}^{n}\frac{\frac{\eta_1}{c}-\cos(y_i-\beta_i X_i)}{c-\eta_1\cos(y_i-\beta_i X_i)-\eta_2\sin(y_i-\beta_i X_i)} $$

I need a big denominator and numerator.

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You can use the \dfrac (displaystyle fraction) command from amsmath or \mfrac (medium-sized fraction, ca 80% of displaystyle) (from nccmath):

\documentclass{article}
\usepackage[utf8]{inputenc}}
\usepackage{mathtools, nccmath}


\newcommand*{\e}{\mathrm{e}}

\begin{document}

\[ \frac{\partial \mathcal{L}}{\partial \eta_1}= -\sum_{i=1}^{n}\frac{\dfrac{\eta_1}{c}-\cos(y_i-\beta_i X_i)}{c-\eta_1\cos(y_i-\beta_i X_i)-\eta_2\sin(y_i-\beta_i X_i)} \]%

 \[ \frac{\partial \mathcal{L}}{\partial \eta_1}= -\sum_{i=1}^{n}\frac{\mfrac{\eta_1}{c}-\cos(y_i-\beta_i X_i)}{c-\eta_1\cos(y_i-\beta_i X_i)-\eta_2\sin(y_i-\beta_i X_i)} \]%

  \[ \frac{\partial \mathcal{L}}{\partial \eta_1}= -\sum_{i=1}^{n}\frac{\frac{\eta_1}{c}-\cos(y_i-\beta_i X_i)}{c-\eta_1\cos(y_i-\beta_i X_i)-\eta_2\sin(y_i-\beta_i X_i)} \]%

\end{document} 

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