How Does the Derivative of sin(x) Equal cos(x)?

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Homework Help Overview

The discussion revolves around understanding the derivative of the sine function, specifically proving that the derivative of sin(x) equals cos(x) using the definition of a derivative. The subject area is calculus, focusing on derivatives and limits.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants express confusion about the definition of the derivative and its application to the sine function. Some attempt to recall the limit definition but struggle with its components, particularly the variable h. Others question their understanding of limits and how they relate to the problem at hand.

Discussion Status

The discussion is ongoing, with participants seeking clarification on fundamental concepts like limits and the derivative. Some guidance has been offered, including references to additional resources, but there is no clear consensus or resolution yet.

Contextual Notes

There appears to be a lack of foundational knowledge regarding limits, which is affecting participants' ability to engage with the problem. The original poster expresses uncertainty about the homework assignment, suggesting it may be beyond their current understanding.

Wholewheat458
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Homework Statement


Prove using the definition of a derivative.
If y=sinx, then y1=cosx


Homework Equations


.. ? identities maybe..? i don't really know much about derivatives..


The Attempt at a Solution


y = sinx..
y1 = (1)sinx^1-1
y1 = 1..
how is that suppose to equal cosx?? !
i haven't got a clue, any help would really be appreciated!
:shy:
 
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What is the definition of the derivative?
 
?? I'm not all that certain..
its got somethink to do with graphs, but..
idk, i been looking at a graph of y = sinx
but i don't know what to do with it: oy
 
.. ?
woahw.. so... how do i apply that
to the sin graph?..
: no clue..
maybe i'll go over it again..
 
You set f(x)=sin(x) in the expression [tex]f'(x)=\lim_{h\to0}\;\frac{f(x+h)-f(x)}{h}[/tex]Hint: if you actually read through that thread, then you may be surprised as to what you find...[/color][/size]

I'm moving this to calc&beyond, since it is calculus!
 
.. i don't think i understand the formula..
: f(x) = sinx .. then.
= sinx = lim(h-->) sin(x+h) - sinx/ h
... this is so wrong
wait, what is h?..
 
Have you studied limits before? From your posts here, it sounds like you haven't. This problem will be incredibly difficult if you have not heard about limits before, and I can't see why it would have been set for you to try.
 
^^ i don't know why either!
ahhahaa! i think i'll just skip it for now..
thanks for your help
 
  • #10
Try learning limits, then the definition of derivative, then the squeeze theorem and then you should be able to make a fairly decent proof of it.
 
  • #11
Wholewheat458 said:
^^ i don't know why either!
ahhahaa! i think i'll just skip it for now..
thanks for your help

Skipping is not possible if you are learning about derivatives right now.
This will haunt you later :blushing:
 

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