How may I derive this equation?

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In summary, the conversation discusses deriving the function y=cos^3(sinx) and the confusion surrounding the use of the chain rule. The correct solution is -3cosxsin(sinx)cos^2(sinx), which is obtained by using the chain rule multiple times and rewriting the function as y=[cos(sinx)]^3. The person asking the question was initially unsure about the question, but eventually arrives at the correct solution with the help of the chain rule.
  • #1
staka
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How may I derive y=cos^3(sinx)?
I thought simply just y=3cos(sinx)^2(cosx)...

Answer given is -3cosxsin(sinx)cos^2(sinx) but no idea how to get to that.
 
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  • #2
I am a bit confused about what the exact question is. What is it?
 
  • #3
How to derive the function: y=cos^3(sinx) is my question... solving for y'=.
 
  • #4
I think you didn't use the chain rule enough times.
You need the derivative of cos3(sin(x)) with respect to cos(sin(x)) times the derivative of cos(sin(x)) wrt sin(x) times the derivative of sin(x) wrt x.
 
  • #5
By derive you mean differentiate, right?

Try writing t=sinx, then y=[cos(t)]^3. Then, dy/dx=(dy/dt)(dt/dx). Course, you need to use the chain rule again when differentiating y wrt t.
 
  • #6
Alright. I'll retry.. solving.
 
  • #7
Oh, differentiate now I know what you are trying to do. Are you familiar with the chain rule?
 
  • #8
I am familar with the chain rule.. I'll retry.
 
  • #9
Alright thanks. I've solved it correctly.
 

1. How do I derive an equation?

To derive an equation, you must first identify the variables and constants involved. Then, use mathematical principles such as the laws of algebra and calculus to manipulate the equation until you reach a desired form. This process involves understanding the concepts behind the equation and applying them correctly.

2. What is the purpose of deriving an equation?

The purpose of deriving an equation is to better understand the relationship between different variables and how they affect each other. It also allows for the prediction of outcomes and the ability to make modifications to the equation for different scenarios.

3. Can I derive an equation without prior knowledge of the subject?

No, deriving an equation requires a solid understanding of the subject and its principles. Without this knowledge, it is difficult to identify the correct variables and use the appropriate mathematical techniques to manipulate the equation.

4. How long does it take to derive an equation?

The time it takes to derive an equation varies depending on the complexity of the equation and the familiarity with the subject. It can take anywhere from a few minutes to several hours or even days to derive an equation.

5. What are some tips for effectively deriving an equation?

Some tips for effectively deriving an equation include clearly defining the variables, using mathematical principles correctly, and checking your work for accuracy. It can also be helpful to break down the equation into smaller, more manageable parts and to seek assistance from experts or references if needed.

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