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

1 Answer
Sep 27, 2016

Answer:

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

Explanation:

#f(g(x)#

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

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

Using chain rule,

#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)#