How do you find the derivative of # y = cosx(cotx)#?

1 Answer
Euan S.
Jul 20, 2016

#(dy)/(dx) = cosx(-csc^2x-1)#

Explanation:

We have to use the product rule.

#d/(dx)(uv) = u(dv)/(dx) + (du)/(dx)v#

#(dy)/(dx) = cosx(d/(dx)(cotx)) + d/(dx)(cosx)cotx#

#= -cosxcsc^2x - sinxcotx#

Remember that #cotx = 1/tanx = cosx/sinx#

#therefore (dy)/(dx) = =-cosxcsc^2x - cosx#

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