How do you differentiate #3sin^2(3x) # using the chain rule?

1 Answer
May 25, 2018

Answer:

#18sin(3x)cos(3x)#

Explanation:

chain rule for 3 functions is #d/dx(f(g(h(x))))=f'(g(h(x)))*d/dx(g(h(x)))=f'(g(h(x)))g'(h(x))h'(x)#

in this problem, #f(x)=3x^2#, #g(x)=sin(x)#, and #h(x)=3x#
that means: #f'(x)=6x#, #g'(x)=cos(x)#, and #h(x)=3#

so #d/dx(3sin^2(3x))=6(sin(3x))*cos(3x)*3#
#=18sin(3x)cos(3x)#