Understanding Total Derivative: Step-By-Step Guide

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The discussion focuses on understanding the total derivative in the context of a specific example involving a function D(p(a)) and its relationship to S(p(a), a). The total derivative with respect to 'a' is expressed using the chain rule, highlighting the relationship between the derivatives of the functions involved. Participants clarify that the total derivative incorporates both the direct and indirect effects of changes in 'a' on 'D'. The key takeaway is that the total derivative can be computed by applying the chain rule to the given functions. This explanation emphasizes the importance of understanding how variables interact in multivariable calculus.
Tom McCurdy
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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}
 
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It's just the chain rule.
 

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