Derivative of Trigonometric Function: y=5sin(0.5x+2)+6

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Homework Help Overview

The problem involves finding the derivative of the function y=5sin(0.5x+2)+6, which is situated within the context of calculus, specifically focusing on the differentiation of trigonometric functions.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of the chain rule and the sum rule in differentiation. There is an attempt to clarify the steps involved in deriving the function, with some questioning the correctness of the initial derivative presented.

Discussion Status

The discussion reflects a progression through various interpretations of the derivative process, with participants offering guidance on applying differentiation rules. There is no explicit consensus reached, but a simplified form of the derivative is suggested by one participant.

Contextual Notes

Participants note the importance of correctly applying differentiation rules, particularly in relation to the constant term in the function. There is an acknowledgment of potential confusion regarding the initial derivative calculation.

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Homework Statement


Find the derivative of y=5sin(0.5x+2)+6


Homework Equations


My initial assumptions would be to use the chain rule.


The Attempt at a Solution


y=5sin(0.5x+2)+6
The chain rule is to take the derivative of the outer function and multiply by the derivative of the inner function.
y'=[5cos(0.5x+2)+6]*[0.5]
y'=[5cos(0.5x+2)+6]/2

But I know this isn't right..
 
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First use the rule for a sum. The derivative of 6 is zero.
 
SammyS said:
First use the rule for a sum. The derivative of 6 is zero.

So...
y'=5cos(0.5x+2)*0.5 ?
 
Yes. And, simplified it would be y' = 2.5 * cos(0.5x + 2)
 

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