deletions | additions       diff --git a/Ellipsens_ekvation_E_x_frac__.tex b/Ellipsens_ekvation_E_x_frac__.tex  index da36e8d..7f46549 100644  --- a/Ellipsens_ekvation_E_x_frac__.tex  +++ b/Ellipsens_ekvation_E_x_frac__.tex 
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We can formulate this as  $$\frac{e_k^2}{e_k^2 + t} y_k = x_k, \qquad k=1,2,3$$  We plug this into the expression for $E$,  $$\frac{y_1^2}{t+e_1^2}+\frac{y_2^2}{t+e_2^2}+\frac{y_3^2}{t+e_3^2}-1=0$$ $$E(t)=\frac{y_1^2}{t+e_1^2}+\frac{y_2^2}{t+e_2^2}+\frac{y_3^2}{t+e_3^2}-1$$  The derivative of the left hand expression above:  $$-\frac{y_1^2}{(t+e_1^2)^2} $$E'(t)=-\frac{y_1^2}{(t+e_1^2)^2}  - \frac{y_2^2}{(t+e_2^2)^2} - \frac{y_3^2}{(t+e_3^2)^2}$$