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

[Wholewheat458]

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:

 

[cristo]

What is the definition of the derivative?

 

[Wholewheat458]

?? 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

 

[cristo]

Here's a thread in our very own learning materials forum. Have a read and then try the question again: https://www.physicsforums.com/showthread.php?t=139690

 

[Wholewheat458]

.. ?
woahw.. so... how do i apply that
to the sin graph?..
: no clue..
maybe i'll go over it again..

 

[cristo]

You set f(x)=sin(x) in the expression f'(x)=\lim_{h\to0}\;\frac{f(x+h)-f(x)}{h}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!

 

[Wholewheat458]

.. 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?..

 

[cristo]

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.

 

[Wholewheat458]

^^ i don't know why either!
ahhahaa! i think i'll just skip it for now..
thanks for your help

 

[Feldoh]

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.

 

[rootX]

^^ 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