Asked by Anonymous
                r=log(cos^2(4theta)) what is the derivative of this?
            
            
        Answers
                    Answered by
            Steve
            
    just use the chain rule:
let r = log(u)
dr/dθ = 1/u du/dθ
let u = cos^2(v)
du/dθ = 2cosv(-sinv) dv/dθ
let v = 4θ
dv/dθ = 4
So, dr/dθ = sec^2(4θ) (-2cos4θsin4θ) (4)
= -8tan4θ
Or, you could just recall that
log(cos^2(4θ)) = 2log cos 4θ
so a simpler application of the chain rule would be
2/cos4θ (-4sin4θ)
= -8tan4θ
    
let r = log(u)
dr/dθ = 1/u du/dθ
let u = cos^2(v)
du/dθ = 2cosv(-sinv) dv/dθ
let v = 4θ
dv/dθ = 4
So, dr/dθ = sec^2(4θ) (-2cos4θsin4θ) (4)
= -8tan4θ
Or, you could just recall that
log(cos^2(4θ)) = 2log cos 4θ
so a simpler application of the chain rule would be
2/cos4θ (-4sin4θ)
= -8tan4θ
                                                    There are no AI answers yet. The ability to request AI answers is coming soon!
                                            
                Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.