I have a function $$ LogC= (LogA - 0.80 * LogB - 8.40)/0.50 $$ Here i have error values for LogA and LogB. So i want to calculate error of LogC. I'm using the formula: $$\Delta LogC=\sqrt{(\frac{\partial LogC}{\partial LogA} * \Delta LogA)^2+(\frac{\partial LogC}{\partial LogB} * \Delta LogB)^2}$$ But the error values goes so high that makes me think that i'm using the formula wrong. So there are 2 options and want to know which one is correct.
1: $$\Delta LogC=\sqrt{(\frac{1-0.80*LogB-8.40}{0.50}* \Delta LogA)^2+(\frac{LogA-0.80-8.40}{0.50} \Delta LogB)^2}$$ or just 2: $$\Delta LogC=\sqrt{(\frac{1}{0.50}* \Delta LogA)^2+(\frac{1-0.80}{0.50} * \Delta LogB)^2}$$
So I thought that partial derivatives would be like in the first example. however, in this way error values look so absurd. You could suggest another better way to calculate error values