The differentiation of `cotx` with respect to `x ` is`-cos e c^2xdot` i.e. `d/(dx)(cotx)=-cosec^2x`

Explanation

Given,
`(d/dx)​cotx=(d/dx)​(cosx)/(sinx)​`
=`(sinx(d/dx)​cosx−cosx(d/dx)​sinx)/(sin^2x)​`
=`(sinx(−sinx)−cosx(cosx)​)/(sin^2x)`
​
=`(−(sin^2x)−(cos^2x))/(sin^2x)​​`

=`−1/(sin^2x)​​=− cosec^2x.`