What's Lagrangian multiplier and when to use it?

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I have this equation $ e^TCe $ with $ e^Te = 1 $ which i want to apply on it lagrange multiplier, how to do it (with steps please) Also how to take the derivative of the lagrangian ?

EDIT : lagrange multiplier is used to create L then derivative of L is calculated with : $\partial L / \partial e$

EDIT2 : C $ \in R^{d*d} $ and e is $ \in R^{p*d} $

EDIT3 :

$$\eqalign{ L &= e^TCe - \lambda(e^Te-1) \cr dL &= de^TCe + e^TC\,de - 2\lambda e^T\,de \quad (1) \cr &= e^TC^T\,de + e^TC\,de - 2\lambda e^T\,de \quad (2) \cr &= 2e^TC\,de - 2\lambda e^T\,de \cr &= 2(Ce-\lambda e)^T\,de \cr \frac{\partial L}{\partial e} &= 2(Ce-\lambda e) \cr }$$

But still can't understand why to go from line (1) to (2) ? THanks