How do you differentiate f(x)=csc3(2x)?

1 Answer
Dec 14, 2016

6tan2xcsc32x

Explanation:

f(x)=csc3(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)
=6cot2xcsc32x

-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