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

Find dP/dV

Answer 1

if c , n , R and T are constant then
P c V^(c-1)dV + V ^c dP = 0
P c V^c dV/V + V^c dP = 0
P c dV + V dP = 0
P c + V dP/dV = 0
dP / dV = -P c/ V

Answer 2

Thank you so much Damon, this has gotten me closer to understanding this type of problem however I get a memo:

"V cannot be part of the answer"

Answer 3

oops it was a matter of Case, thank you!