Deriving the Formula y = arcsinh(x)

[Miike012]

Question:
Derive the formula y = arcsinh(x), the inverse hyperbolic function.

I thought the question was asking to find the derivative of the inverse function but my teacher marked it 0/10 points because he did not want the derivative...

Can "derived" mean derivative? If so...

Is there a way that I can argue that this question was poorly phrased?

Thank you.

 

[LCKurtz]

Question:
Derive the formula y = arcsinh(x), the inverse hyperbolic function.

I thought the question was asking to find the derivative of the inverse function but my teacher marked it 0/10 points because he did not want the derivative...

Can "derived" mean derivative? If so...

Is there a way that I can argue that this question was poorly phrased?

Thank you.

No. He said "derive the formula" not "differentiate it".

 

[lurflurf]

http://dictionary.reference.com/browse/derive

The teacher and LCKurtz are in need of dictionaries and better manners. Derive and differentiate are synonyms, like factor and factorize or add and sum. Confusion may result because derive has other meanings. It is a badly worded question, however differentiate the function is the best interpretation because if derive was meant in another way there should have been context. Maybe the teacher does not know what a derivative is.

Perhaps if there was some contest in the test somewhere.

 

[LCKurtz]

http://dictionary.reference.com/browse/derive

The teacher and LCKurtz are in need of dictionaries and better manners. Derive and differentiate are synonyms, like factor and factorize or add and sum. Confusion may result because derive has other meanings. It is a badly worded question, however differentiate the function is the best interpretation because if derive was meant in another way there should have been context. Maybe the teacher does not know what a derivative is.

Perhaps if there was some contest in the test somewhere.

I have never seen a calculus text where the statement "derive the formula" meant differentiate it. It certainly is not common usage in US calculus books. Can you even show me one reference to such?

 

[berkeman]

http://dictionary.reference.com/browse/derive

The teacher and LCKurtz are in need of dictionaries and better manners. Derive and differentiate are synonyms, like factor and factorize or add and sum. Confusion may result because derive has other meanings. It is a badly worded question, however differentiate the function is the best interpretation because if derive was meant in another way there should have been context. Maybe the teacher does not know what a derivative is.

Perhaps if there was some contest in the test somewhere.

I agree with LCKurtz -- at least in the US, "derive" doesn't mean differentiate. Perhaps we should just chalk this up to the PF being an international website, with different terms being used in different countries.

 

[romsofia]

If I was to ask you to derive the Fourier series for some function, would you take the derivative of it? I sure wouldn't.

Sorry, but you have no leeway with an argument on this one.

 

[Dick]

If somebody asked me "Derive the formula y = arcsinh(x), the inverse hyperbolic function." I would first say "derive from what?". If I couldn't get an answer (as lurflurf said, if there is no other context) I'd probably guess derive meant 'differentiate', since I've seen it used that way at least casually. If that's the whole problem, I'd have no idea what else to do. I'm guessing this is probably part of a larger problem if there is an alternative answer.

 

[berkeman]

http://dictionary.reference.com/browse/derive

The teacher and LCKurtz are in need of dictionaries and better manners. Derive and differentiate are synonyms, like factor and factorize or add and sum. Confusion may result because derive has other meanings. It is a badly worded question, however differentiate the function is the best interpretation because if derive was meant in another way there should have been context. Maybe the teacher does not know what a derivative is.

Perhaps if there was some contest in the test somewhere.

lurflurf -- would you acknowledge that the term "derive" would appear to have different meanings in different countries, and that your comment about "bad manners" may not be applicable here? I certainly would not have meant anything bad by not understanding the use of "derive" in this thread if I had responded to the technical question.

 

[romsofia]

If somebody asked me "Derive the formula y = arcsinh(x), the inverse hyperbolic function." I would first say "derive from what?".

They're plenty of ways you could derive it, but I'm assuming the prof. was looking for one to be using the definition of y=sinh(x)=(e^x-e^-x)/2 and then substituting x=y, so you'll have x=sinh(y)=(e^y-e^-y)/2 and then solving for y from there.

So it doesn't matter how you derive it, as long as you do derive it.

 

[LCKurtz]

They're plenty of ways you could derive it, but I'm assuming the prof. was looking for one to be using the definition of y=sinh(x)=(e^x-e^-x)/2 and then substituting x=y, so you'll have x=sinh(y)=(e^y-e^-y)/2 and then solving for y from there.

That is certainly how I would respond to the question and I will bet that is what the OP's teacher expected.

@Mike012 -- Is that what your teacher expected you to do?