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What is the derivative of #T(w)=cot^3(3w+1)#?

Answer 1

Ezekiel Alexander

#T^'(w)=-9cot^2(3w+1)csc^2(3w+1)#

We know that,

#color(red)((1)d/(dx)(x^n)=nx^(n-1)#

#color(red)((2)d/(dx)(cotx)=-csc^2x#

Here,

#T(w)=cot^3(3w+1)=(cot(3w+1))^3#

Diff.w.r.t. '#w#'

#T^'(w)=3(cot(3w+1))^2d/(dw)((cot(3w+1))...toApply(1)#

#=3cot^2(3w+1)(-csc^2(3w+1))d/(dw)(3w+1).toApply(2)#

#=-3cot^2(3w+1)csc^2(3w+1)(3)#

#=-9cot^2(3w+1)csc^2(3w+1)#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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