Total derivative of a composite function with respect to parameter a

[Tom McCurdy]

Hi I was hoping someone could explain how this works to me

I ran across this example in a book

D(p(a)) = S(p(a),a)
Total derivative with respect a

$$\frac{dD(p(a))}{dp} \frac{dp}{da}= \frac{\partial S(p(a),a)}{\partial p} \frac{dp}{da} + \frac{\partial S(p(a),a)}{\partial a}$$

 

[HallsofIvy]

It's just the chain rule.