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Derivatives: How to Find
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The
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Derivatives of Trig Functions
When you were a kid, there were two key facts to remember, your name and your address. You
confused the two, and you might have been lost forever. You're not a kid anymore, but in this
section, there are still just two key facts to remember that you don't want to mix up, namely:
and
The derivatives of all of the other trig functions follow from these.
It is easy to get confused about which of these two derivatives has the negative sign in front. The
easiest way to keep it straight is to remember,
``Sine keeps its sign, when you differentiate".
That is to say, when you differentiate the sine function, you do not change the sign for the result.
I guess you could remember, ``Cosine changes sign," but it's not as catchy.
Showing that the derivative of the sine and cosine functions are what they are by using the limit
definition of the derivative is a little tricky. It uses the fact that we already made a big deal over,
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 Trigonometry, Derivatives, Derivative, Mathematical analysis, Euler's formula

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