Question

Partial Derivative word problem: http://imgur.com/Qav2V

Could anyone tell me whether part a is right and help with part b?

Answer 1

A is correct, think about what causes more influence and dependence inside of a function?

Answer 2

For dA/dh it's -22.4+1.2t not -1.2t

Answer 3

oh yes dont mess up on keeping your signs correct

Answer 4

b is kind of a weird question. It's like asking which one is more one second or three pounds.

Anyway, I guess they mean which partial derivative is bigger and expect you to ignore units.

The answer depends on the values of t and h. I.e for some temperatures one unit of change in t matters more, for some one unit of change in h does. Not sure if that helps.

Answer 5

To clarify, I'd try to determine for which points (t,h) is dA/dt>dA/dh

I'm writing dA/dt but I mean partial derivatives of course.

Answer 6

Hmm, so dA/dh (a change in humidity) effects air temp more because dA/dh > dA/dt (air temp is a higher value when we change just humidity and not temp than when we change temp and not humidity?)

That doesnt really make sense to me...

Answer 7

I feel like I need to plug in more values to something and do a different comparison

Answer 8

pay attention to the original function and the weights connected to each variable, weights are the scalars that they are multiplied by, the heavier weight means more influence...

Answer 9

so -22.4h

Answer 10

Whats the point of finding the partial derivative then?

Answer 11

because you can see how large it actually changes by when you find some derivative of a measurement.

Answer 12

Ask yourself the question: How much does the apparent temperature change if the humidity changes by one unit? What if the actual temperature changes by one unit?