What is $\frac{d}{dx}\left(\cot 4x\right)$ for $0 < x < \frac{\pi}{4}$?

Explanation

1. 01

   $\frac{d}{dx}\cot u = -\operatorname{cosec}^{2} u \cdot u'$ with $u = 4x$.

2. 02

   $-\operatorname{cosec}^{2} 4x \cdot 4 = -4\operatorname{cosec}^{2} 4x$.