Chain Rule for Derivatives: cos(tan(pi x))^1/2

[asz304]

I had my midterm earlier today, and I can't stop thinking about this question

cos*(tan pi*x)^1/2

Is it right if I used the chain rule? And in my mind I think that the question was meant to be cos(tan(pi x))^1/2 and not cos(1)*(tan pi*x)^1/2 which will then be the result of using the product rule and chain rule.

 

[micromass]

I'm sorry, but cos*(tan pi*x)^1/2 doesn't make any sense. Probably a typo, but of what value do you take the cosine?

Is it cos(1)*(tan pi*x)^1/2 ? then you will have to use the product rule and the chain rule.
Is it cos((tan pi*x)^1/2), then you will have to use the chain rule several times...

 

[asz304]

I'm sorry, but cos*(tan pi*x)^1/2 doesn't make any sense. Probably a typo, but of what value do you take the cosine?

Is it cos(1)*(tan pi*x)^1/2 ? then you will have to use the product rule and the chain rule.
Is it cos((tan pi*x)^1/2), then you will have to use the chain rule several times...

The question that showed up in the exam was cos*(tan pi*x)^1/2. or " Cosine times the square root of tangent pi x". I'm not sure if you can call it "times" since cosine is just beside the square root of tangent pi x.

 

[micromass]

But that makes no sense? how can you multiply cos with something?? cos is a function, not a number...

 

[asz304]

But that makes no sense? how can you multiply cos with something?? cos is a function, not a number...

Yeah, so I decided to consider that cos*(tan pi*x)^1/2 is cos ( tan (pi * x ) )^1/2.

Notice also the original tangent it's just tan pi*x not tan (pi*x).

 

[micromass]

Wow, that sucks to have that as an exam question... You don't even know what they mean...

 

[asz304]

Wow, that sucks to have that as an exam question... You don't even know what they mean...

Yes..especially if the midterm had only 4 questions...sigh...if I didn't get this question I'll get a 75.

 

[ZenOne]

I believe this would just be a multiple chain rule problem.

Namely:

-sin*(tan pi x)^1/2 * 1/2*(tan pi x)^1/2 * sec^2 pi x * pi

This can be simplified of course. I'm fairly certain that's the answer. There would be no product rule because there only is one x--it would strictly be chain rule.