Question

Using the definition of a derivative, can you work out the derivative of Cos(x)?

Answer 1

\[\lim_{h\rightarrow0}{\frac{\cos(x+h)-\cos(x)}{h}}\]

Answer 2

\[\text{Recall that }\cos(a+b) = \cos(a)\cos(b) - \sin(a)\sin(b)\]

Answer 3

\[= \lim_{h \rightarrow 0} \frac{ \cos(x) [ \cos(h)-1] }{h} - \lim_{h \rightarrow 0} \frac{\sin(h)}{h} \sin(x)\]

Answer 4

lol, all the working out and put -cos(x) on the last line.

Answer 5

Thanks guys, that was helpful. Do you think you could also help me with finding the derivatives of tan(x), sec(x), csc(x), and cot(x)??

Answer 6

derivatives for those? :-(

Answer 7

yea, its for my calc class, and nobody knows how to do it...

Answer 8

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Answer 9

ok... that sounds simple enough

Answer 10

I mean -sin(x) sorry...

Answer 11

Thank you everybody, you've really saved me here.