What is the derivative of #arctan (cos 2t)#?

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Answer 1 · 2018-04-04T15:44:40

# -2sin(2t)/(cos(2t)^2+1)#

The derivative of #tan^-1(x)# is #1/(x^2+1)#

when we substitute #cos(2t)# for x we get

#1/(cos(2t)^2+1)#

Then we apply the chain rule for cos(2t)

#1/(cos(2t)^2+1) * -2sin(2t)#

Our final answer is

# -2sin(2t)/(cos(2t)^2+1)#