Calculate the derivatives $sin^{'}(x) = \frac{d}{dx}sin(x) and cos^{'}(x) = \frac{d}{dx}cos(x)$
by differentiating the summands of the power series. Show as a corollary the identity
$sin^{2}(x)+cos^{2}(x) = 1$ for all $x \in \mathbb{R}$.

Question

Calculate the derivatives $sin^{'}(x) = \frac{d}{dx}sin(x) and cos^{'}(x) = \frac{d}{dx}cos(x)$
by differentiating the summands of the power series. Show as a corollary the identity
                  $sin^{2}(x)+cos^{2}(x) = 1$ for all $x \in \mathbb{R}$.

anonymous · Answer

$$\sin^{'}(x) = \frac{d}{dx}\sin(x) and \cos^{'}(x) = \frac{d}{dx}\cos(x)$$

anonymous · Answer

ah
ok
you want to write the power series, which is pretty easy, and then take the derivative of each of the terms
then simplify and see what the power series now resembles

anonymous · Answer

Well it comes out to be cos x for the first one
-sin x for the second one

anonymous · Answer

i it possible to solve it ? i am quite bad at mathematics.. :(

anonymous · Answer

@tunahan look at what i just said

anonymous · Answer

ok thx..

anonymous · Answer

if you need more help just ask, k?

anonymous · Answer

also it would help me more if i would see the solution, and try too understand it, because tomorrow i must give up this homework, and there is 3 more questions, i dont know if i can finish it until give up time... there is 5 more questions to do .

anonymous · Answer

well do you know how to write a power series?

anonymous · Answer

i am sorry as i said my math is really sucks, i am computer science student and i had always problem with math...

anonymous · Answer

http://www.khanacademy.org/math/calculus/v/sine-taylor-series-at-0--maclaurin watch this first then

anonymous · Answer

ok..

anonymous · Answer

http://www.khanacademy.org/math/calculus/v/taylor-polynomials or this and then write the taylor series

anonymous · Answer

@cerezas i have looked , but it will take me time understand it hole, i am in germany and in about 8 hours i must finish my homework :( its better if you can solve it for me, and in one month i have exam i will ask you every details of it if you will be here ;)

anonymous · Answer

i need 16 points if i have less then 8 points i think i cant participate at final exam

anonymous · Answer

http://www.wolframalpha.com/input/?i=taylor+series+sin+x&lk=3 now take the derivative, simplify, and that's cosx

anonymous · Answer

ok thx

anonymous · Answer

sure