How do you differentiate #f(x)=csc^3(2x)#?

1 Answer
Alexander L.
Dec 14, 2016

#-6tan2xcsc^3 2x#

Explanation:

#f(x)=csc^3(2x)=(sin2x)^-3#

Now that we see the #sin2x# instead of #csc2x# term, it is pretty straight forward from here.

#(df(x))/(dx)=-3(sin2x)^-4(cos2x)(2)#
#=-6cot2xcsc^3 2x#

-The #-3# comes from the power.
-The power #-4# is because of the differentiation.
-The #cos2x# because you want to differentiate #sin2x# in the bracket.
-The #2# because you differentiate #2x#.

Cheers

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