Question #b8918

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Answer 1 · 2017-07-16T18:03:13

#d/(dx) [cot(3x^2-7)] = color(blue)(-6xcsc^2(7-3x^2)#

We're asked to find the derivative

#(dy)/(dx)[y = cot(3x^2-7)]#

#y'(x) = d/(dx)[-cot(7-3x^2)]#

Factor out the #-1#:

#= -d/(dx)[cot(7-3x^2)]#

Use the chain rule:

#d/(dx) [cot(7-3x^2)] = d/(du) [cotu] (du)/(dx)#

where

#= -(-csc^2(7-3x^2) d/(dx)[7-3x^2])#

#= csc^2(7-3x^2) d/(dx)[7-3x^2]#

#= color(blue)(csc^2(7-3x^2)(-6x)#