If #f(x)= sin6x # and #g(x) = sqrt(x+3 #, how do you differentiate #f(g(x)) # using the chain rule?

1 Answer
May 30, 2017

Answer:

#d/dx[f(g(x))] = (3cos(6sqrt(x+3)))/sqrt(x+3)#

Explanation:

#f(x) =sin(6x)#
#g(x)=sqrt(x+3)#

#:. f(g(x)) = sin(6sqrt(x+3))#

Applying the Chain Rule

#d/dx[f(g(x))] = cos(6sqrt(x+3)) * d/dx(6sqrt(x+3))#

#= cos(6sqrt(x+3)) * d/dx 6(x+3)^(1/2)#

Applying the Power Rule

#= cos(6sqrt(x+3)) * (6(x+3)^(-1/2))/2#

# = (3cos(6sqrt(x+3)))/sqrt(x+3)#