If #f(x) =cos3x # and #g(x) = sqrt(3x-1 #, what is #f'(g(x)) #?

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Answer 1 · 2016-09-27T07:16:32

#=-(9/2)sin(3 sqrt(3x-1))/(sqrt(3x-1)#

#f(g(x)#

#=cos (3 g()x))#

#=cos(3 sqrt(3x-1))#

#f'=(cos(3 sqrt(3x-1))'#

#=-sin(3 sqrt(3x-1))(3sqrt(3x-1))'#

#=-sin(3 sqrt(3x-1))((-3/2)/(sqrt(3x-1)))(3x-1)'#

#=-sin(3 sqrt(3x-1))((-3/2)/(sqrt(3x-1)))(3)#

#=-(9/2)sin(3 sqrt(3x-1))/(sqrt(3x-1)#