#Calc trig differentiation question

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dreamy crown
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I’m not sure where I went wrong when doing this question, where did the negative in the answer come from? Am I substituting something and forgetting the negative? Question and answer as well as the work that I did in photos. Can someone please explain for me, thanks!

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stone questBOT
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dreamy crown
dreamy crown
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problem area circled^

valid lodge
# dreamy crown

Let's differentiate cot(x) from scratch. cot(x) = cos(x)/sin(x), right?

dreamy crown
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Yes

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And then the differentiated version of cot x = csc2x is my understanding

valid lodge
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So using the quotient rule, what do we get?

dreamy crown
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Ok so then: (-sinx sinx - cosx cosx)/sin2x

valid lodge
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And then the numerator is?

dreamy crown
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-sin2x-cos2x

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oh so then sin2x cancels so it’s -cos2x

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wait not quite just a sec

valid lodge
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...what's sin^2(x) + cos^2(x)?

dreamy crown
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1

valid lodge
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Therefore...?

dreamy crown
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-1

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So then -1/sin2x

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then -csc2x so I was missing a negative

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okay thank you

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+close

lyric larkBOT
# dreamy crown +close
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lyric larkBOT
# lyric lark

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