# How Do You Differentiate Complex Trigonometric Functions?

• duki
In summary, the conversation discusses finding the derivative of the function y = [cos^6 ( csc^2(4e^\pi^3))]^\frac{23}{15}. After attempting a solution, it is determined that the derivative is 0 because y is a constant independent of x. The conversation ends with the understanding that, in a similar problem on a test, it can be stated that y is a constant and therefore the derivative is 0.
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?

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

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.

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.

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."

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.

Alright cool. Thanks :)

## 1. What is a derivative?

A derivative is a mathematical concept that represents the instantaneous rate of change of one variable with respect to another. In simpler terms, it measures how much one variable changes in response to a change in another variable.

## 2. Why are derivatives important?

Derivatives are important because they have many practical applications in various fields, such as physics, economics, and engineering. They are used to calculate rates of change, optimize functions, and solve complex problems.

## 3. How do you find a derivative?

To find a derivative, you need to use a specific mathematical formula called the derivative rule. This rule involves taking the limit of a ratio of change in the function over a small interval. There are also different rules for finding derivatives of different types of functions, such as polynomials, trigonometric functions, and exponential functions.

## 4. What are some common problems with derivatives?

Some common problems with derivatives include difficulty in understanding the concept, confusion with notation, and making mistakes when applying the derivative rule. It is important to practice and review the rules and concepts to avoid these problems.

## 5. How can I improve my skills in solving derivative problems?

To improve your skills in solving derivative problems, it is important to practice regularly and use different resources, such as textbooks, online tutorials, and practice problems. It is also helpful to understand the underlying concepts and rules rather than just memorizing formulas.

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