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

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Answer 1 · 2018-03-27T19:46:44

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

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. ' $w$ '

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

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

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

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

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