# Why $(\frac{\partial S}{\partial T})_P=(\frac{\partial S}{\partial T})_V+(\frac{\partial S}{\partial V})_T(\frac{\partial V}{\partial T})_P$?

In the thermodynamics book (Adkins) I'm using, the following relation is cited without reference but I am not sure where it comes from.

$$\left(\frac{\partial S}{\partial T}\right)_P=\left(\frac{\partial S}{\partial T}\right)_V+\left(\frac{\partial S}{\partial V}\right)_T\left(\frac{\partial V}{\partial T}\right)_P$$

I am not sure what combination of mathematical and physical relations leads to this but any help would be appreciated!

Here, $$S$$ is a function of $$V$$ and $$T$$. Here, we want to know $$\left (\frac{\partial S(V,T)}{\partial T} \right )_P$$.
By chain rule, $$\left (\frac{\partial S(V,T)}{\partial T} \right )_P = \left (\frac{\partial S(V,T)}{\partial T} \right )_V\times \left(\frac{\partial T }{\partial T}\right)_P + \left (\frac{\partial S(V,T)}{\partial V} \right )_T\times \left (\frac{\partial V }{\partial T} \right )_P$$.