How do you differentiate #f(x)=cosx(cotx)#?

1 Answer
Nov 4, 2016

Differentiating #f(x)# comes to be #-cosx((1+sin^2x)/sinx).#

Explanation:

Let, #y=f(x)=cosx*cotx#
Therefore Differentiating #y# w.r.t #x# comes to be,

#(dy)/(dx)=d/(dx)(cosx*cotx)#
#:.dy/dx=cosx*d/(dx)(cotx)+cotx*d/(dx)(cosx)#
#:.dy/dx=cosx*(-cosec^2x)+cotx*(-sinx)#
#:.dy/dx=-cosx/sin^2x-cosx=-cosx((1+sin^2x)/sinx).# (answer).