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c3 differentiation of trig functions

I', a bit confused as to how to differentiate with respects to x the following:

cot3xcot^3 x

In my attempt I managed to get (−cosec2x)3(-cosec^2x)^3, which I know is incorrect.

Please could someone advise me on what I need to do in order to get the correct answer?
Reply 1
Avatar for nuodai
nuodai
17
You're on the right track, but you need to use the chain rule. Remember that cot⁡3x=(cot⁡x)3\cot^3 x = (\cot x)^3, so you can make the substitution u=cot⁡xu = \cot x.
ahh, yes, that works now. C:

Much appreciated!
Reply 3
Avatar for maxfire
maxfire
14
y=un[br][br]dydx=n×u′×un−1[br][br]u=1tanx[br] y = u^n[br][br]\dfrac{dy}{dx} = n\times u' \times u^{n-1}[br][br]u = \dfrac{1}{tanx}[br]

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