anonymous
  • anonymous
Greetings! Derrivate of sin(2x+pi) Help is much appreciated ! :)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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Vocaloid
  • Vocaloid
the general format for a sin derivative is d(sinx)/dx = cos(x) * d(x)/d(x) so d(sin(2x+pi)/dx = cos(2x+pi)*d(2x+pi) = cos(2x+pi)*2
Vocaloid
  • Vocaloid
here's an easier way to remember/explain it to find the derivative of sin(a), change the sin to cos, keep the a, then multiply by the derivative of a
Rizags
  • Rizags
wait. think about it... what happens to the graph of sine when you add π

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Rizags
  • Rizags
\[\sin(2x+π) = -\sin(2x)\]
anonymous
  • anonymous
ofc that first equation makes sense, however ur last one, I get but its hard to come to that conclusion, I understand pi jumps 180degrees making it negative, but its not obvious.
Rizags
  • Rizags
therefore we have: \[\large -(\frac{d}{dx}(\sin(2x)))\]
Rizags
  • Rizags
chain rule it^^
anonymous
  • anonymous
u'v+uv'?
Rizags
  • Rizags
right, like so: \[\frac{d}{dx}(\sin(2x))=\frac{dsin(u)}{du}\frac{du}{dx}\] Im going to let \[u=2x\] can you solve now?
anonymous
  • anonymous
cos(u)*2 Then u=2x so gives Cos2x*2. U forgot the pi tho, what happened to it?
Rizags
  • Rizags
as i said before, the π disappears when i rewrite the entire thing as -sin(2x)
Rizags
  • Rizags
and make sure you add the negative from before. The final answer is: \[\huge -2\cos(2x)\]
anonymous
  • anonymous
ah okey, I will remember that, so my first step should always be to get rid of pi? then move on the the chain rule and so forth:) Alright, thank you :)
Rizags
  • Rizags
no prob. Medal please!
Rizags
  • Rizags
yea π is an issue
anonymous
  • anonymous
Haha there ya go, Always fun to learn when things go this smoothly, u explain well:) Cheers!

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