If you look at the picture i uploaded, it shows a graph with two lines. Temp is on the X axis and by reading along from one point on the Y axis you get two different temperatures depending on which line you stop at, Ta or Tb. As shown in the image the average temp To is ; T0 = (Tb + Ta)/2 and what i am presuming is the derivative∂T = 1/2 (Tb - Ta).

Could someone please show me the steps carried out to get from the first equation to the second and where the minus came from. I have not done any maths like this for a long time, so if you could do it in baby steps, i would appreciate it.

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