# Thread: How to apply differentiation rules to T0 = (Tb + Ta)/2

1. ## How to apply differentiation rules to T0 = (Tb + Ta)/2

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.

2. ## How to apply differentiation rules to T0 = (Tb + Ta)/2

This graph has two lines and the X axis is temp.
If you read from one point on the Y axis until you reach a line, you get two X values depending on the line you read off, giving you two temp values Tb or Ta.

The average Temp,T0 therefore equals : T0 = (Tb + Ta) /2
The derivative is shown below it on the picture: ∂T0 = 1/2(Tb - Ta)

Can someone show me how the differentiation rules apply to get from the first equation to the derivative second equation. Please show step by step as i haven't done this in years. Also can you please explain where the minus came from.

Thanks

3. Originally Posted by Schumi

This graph has two lines and the X axis is temp.
If you read from one point on the Y axis until you reach a line, you get two X values depending on the line you read off, giving you two temp values Tb or Ta.

The average Temp,T0 therefore equals : T0 = (Tb + Ta) /2
The derivative is shown below it on the picture: ∂T0 = 1/2(Tb - Ta)

Can someone show me how the differentiation rules apply to get from the first equation to the derivative second equation. Please show step by step as i haven't done this in years. Also can you please explain where the minus came from.

Thanks
What is the context of this problem (i.e. where does this graph come from?)?

What is the x-axis?