Evaluate the derivatives by implicit differentiation. Assume all letters represent constants, except for the independent and dependent variables occurring in the derivative.

Question

𝑃𝑉^𝑐=𝑛𝑅𝑇

Answer 1

Assuming that only c and n are constants, then we have
V^c dP/dT + cPV^(c-1) dV/dT = n(T dR/dT + R dT/dT)

you can replace /dT with any other varying quantity, such as time, etc.

Somehow I don't think this is what you are looking for, but since your question was rather vague, it's the best I can do so far.

All you really need for implicit derivatives is the chain rule, product rule, quotient rule.

Answer 2

Hi oobleck, the question asks for DP/DV, sorry for not including this earlier.

Answer 3

wrong

Answer 4

-c*P/V good