In high school, we studied the related operations of derivatives, including compound functions.

That is, four algorithms of derivative, including:

Derivation rule of 1, function sum (or difference)

2. Derivation rule of function product

3. Derivation rule of function quotient

Your formula above is actually the second case, the derivative rule of function product.

That is, the derivative of the product of two functions is equal to the derivative of the first function multiplied by the second function, plus the derivative of the first function multiplied by the second function.

That is, what general math teachers often say is "lead before, lead after, not lead+lead after, lead before".

The above formula can be seen as DG = DH-D (TS) = DH-(TDS+SDT) = DG = DH-D (TS) = DH-TDS-SDT by subtraction.

But in general, that is, under normal temperature and pressure, dT = 0 (constant temperature).

So: d G= dH-TdS.

You got it? Ask me if you don't understand.