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

Question

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

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Definition of f(h): f(h) is given as the rate of change of the air pressure at a given height above sea level, and it is measured in psi per foot. This means that f(h) represents how much the pressure changes (in psi) for each foot of height (h) change.Derivative f'(h): The derivative f'(h) represents the rate of change of the function f(h) with respect to h. Since f(h) is measured in psi per foot, the derivative f'(h) will measure the rate of change of pressure change with respect to height. In other words, it measures how the rate of pressure change itself changes with each additional foot of height.Units of f'(h): The units of f'(h) will therefore be the units of f(h) divided by the units of h. Since f(h) has units of psi per foot and h has units of feet, the units of f'(h) will be (psi per foot) per foot.Final Measurement: Simplifying the units, we get (psi/foot)/foot which is equivalent to psi/foot^2. This means that f'(h) is measured in psi per square foot.

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