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

Question

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

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Function and Derivative Relationship: The function f(p) measures height in feet for a given pressure in psi. The derivative f'(p) will represent the rate of change of height with respect to pressure. To find the units of f'(p), we need to consider the units of the original function f(p) and the variable p.Units of Original Function: The units of f(p) are feet since it measures height. The variable p is measured in psi, which stands for pounds per square inch. When we take the derivative of f with respect to p, we are essentially dividing a change in height (in feet) by a change in pressure (in psi).Units of Derivative: Therefore, the units of the derivative f'(p) will be the units of height (feet) divided by the units of pressure (psi). This gives us the units of feet per psi.

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