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What is the derivative of #sin(2x)#?

Answer 1

Isabella Ackerman

#2*cos(2x)#

I would use the Chain Rule:

First derive #sin# and then the argument #2x# to get:
#cos(2x)*2#

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Answer 2

Emily Ammerman

#2cos2x#

The key realization is that we have a composite function, which can be differentiated with the help of the Chain Rule

#f'(g(x))*g'(x)#

We essentially have a composite function

#f(g(x))# where

#f(x)=sinx=>f'(x)=cosx# and #g(x)=2x=>g'(x)=2#

We know all of the values we need to plug in, so let's do that. We get

#cos(2x)*2#

#=>2cos2x#

Hope this helps!

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Answer 3

William Abdalla

The derivative of sin(2x) is cos(2x) * 2.

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Answer 4

Emma Aldridge

The derivative of ( \sin(2x) ) with respect to ( x ) is ( 2\cos(2x) ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.