How Do You Differentiate Complex Trigonometric Functions?

[duki]

Homework Statement

Find $$\frac{dy}{dx}$$

Homework Equations

$$y = [cos^6 ( csc^2(4e^\pi^3))]^\frac{23}{15}$$

The Attempt at a Solution

so far I have $$\frac{23}{15}[cos^6 ( csc^2(4e^\pi^3))]\frac{d}{dx}cos^6 ( csc^2(4e^\pi^3))$$... but I stopped here because I don't know if I'm doing it right.

Could someone give me a hand?

 

[Dick]

There's no x in your expression at all. So dy/dx=0. This smells like a trick question.

 

[duki]

HAHA! the answer was actually 0, but I had no clue how to get to it. I remember he did something on the board that I didn't get to copy down where everything ended up canceling out though.

 

[Dick]

y is a constant, independent of x. Of course, dy/dx=0. You don't even have to copy anything down. The fact the expression is so ridiculously complicated should be a clue that someone is trying to pull a fast one.

 

[duki]

So on the test tomorrow, if a problem like this comes up I should be safe saying:

"no 'x' expression exists, therefore dy/dx = 0."

 

[Dick]

No, just say what I said. "y is a constant independent of x, so dy/dx=0". It's just like differentiating y=2. Or y=pi/3. Or $$y = [cos^6 ( csc^2(4e^\pi^3))]^\frac{23}{15}$$. They are all the same thing.

 

[duki]

Alright cool. Thanks :)