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

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To calculate the derivative of y = √sin(x), the initial steps involve applying the chain rule, resulting in y' = 1/2 (sin(x))^(-1/2) (cos(x)). The discussion reveals that both the derived answer and the book's answer, 1/2 cot(x) (√sin(x)), are correct. The relationship between cotangent and sine/cosine is emphasized, as cot(x) = cos(x)/sin(x). Understanding the definitions of cotangent and tangent in terms of sine and cosine helps clarify the equivalence of the two answers. Both approaches yield valid derivatives for the function.
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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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