How Do You Calculate the Derivative of √sin(x)?

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Homework Help Overview

The problem involves calculating the derivative of the function y = √sin(x), which falls under the subject area of calculus, specifically differentiation techniques.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to differentiate the function using the chain rule and presents their calculation. Some participants question the correctness of both the original poster's and the book's answers, while others suggest exploring the definition of cotangent and its relationship to sine and cosine.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the derivative and questioning the validity of the answers presented. There is a mix of agreement and inquiry regarding the definitions and relationships between trigonometric functions.

Contextual Notes

Participants are navigating potential discrepancies between their calculations and the textbook answer, indicating a need for clarification on trigonometric identities and differentiation rules.

domyy
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Homework Statement



y = √sinx


The Attempt at a Solution



y' = [(sinx)1/2]'
y' = 1/2 (sinx)-1/2 (sinx)'
y' = 1/2 cosx (sinx)-1/2

However book says the answer should be:

1/2 cotx (√sinx)
 
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Hint: what is the definition of cotan(x)?
 
Your answer is right. The book's answer is also right. cot(x)=cos(x)/sin(x). Try to convince yourself they are both right.
 
1/tanx ?
 
And what is tan in terms of cos and sin?
 

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