Question #920f7

1 Answer
Aug 10, 2017

#d/(dx) [-csc^2x] = color(blue)(2cotxcsc^2x#

Explanation:

We're asked to find the derivative

#d/(dx) [-csc^2x]#

Let's first use the chain rule:

#d/(dx) [-csc^2x] = -d/(du) [u^2] (du)/(dx)#

where

  • #u = cscx#

  • #d/(dx) [u^2] = 2u#:

#= -2cscxd/(dx)[cscx]#

The derivative of #cscx# is #-cotxcscx#:

#= -2cscx(-cotxcscx)#

Or

#= color(blue)(ulbar(|stackrel(" ")(" "2cotxcsc^2x" ")|)#