The atmospheric pressure of the air changes with height above sea level. The pressure of the air at a given height above sea level can be measured by the differentiable function f(h), in psi, where h is measured in meters. What are the units of f^(')(h) ? psi meters psi / meter meters / psi psi // meter ^(2) meters //psi^(2)

Question

The atmospheric pressure of the air changes with height above sea level. The pressure of the air at a given height above sea level can be measured by the differentiable function  f(h), in psi, where  h is measured in meters. What are the units of  f^(')(h) ? psi meters psi / meter meters / psi psi  // meter  ^(2) meters  //psi^(2)

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Function Derivative Definition: The derivative of a function with respect to a variable gives us the rate of change of the function with respect to that variable. In this case, f(h) represents the atmospheric pressure in psi at a given height h in meters. The derivative f'(h) will therefore represent the rate of change of pressure with respect to height.Units of Derivative: Since f(h) is measured in psi and h is measured in meters, the derivative f'(h) will be measured in units of psi per meter. This is because the derivative will tell us how much the pressure changes (in psi) for a small change in height (in meters).Correct Units for f'(h): The correct units for f'(h) are therefore psi per meter, which can be written as psi/meter or psi // meter.

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