To find: The derivative by implicit function.
The derivative of the equation is .
The equation is , where P is the pressure, V is the volume and T is the temperature of the gas and R, a and b are constants, T remains constant.
Obtain the derivative the equation by using implicit differentiation.
The equation is .
Differentiate implicitly with respect to P,
Apply the product rule and simplify the terms,
Apply the chain rule,
Simplify further and obtain the derivative,
Therefore, the derivative of the equation is .
To find: The rate of change of volume with respect to pressure.
The rate of change of volume with respect to pressure is .
Positive constants .
The value .
Form part (a), the derivative of the equation is .
Substitute , , , and in .
Therefore, the rate of change of volume with respect to pressure is .
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