If #f(x)= sin3x # and #g(x) = -3x #, how do you differentiate #f(g(x)) # using the chain rule?

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Answer 1 · 2018-06-30T21:19:35

#-9cos(9x)#

Let's plug in #g(x)# wherever we see an #x# in #f(x)#. This gives us

#f(g(x))=sin(-9x)#

Now, in our new composite function, we know

#f(x)=sinx=>f'(x)=cosx#

#g(x)=-9x=>g'(x)=-9#

The Chain Rule says that the derivative of a composite function #f(g(x))# will be

#f'(g(x))*g'(x)#

Plugging in our values, we will get

#cos(-9x)*-9#

#=>-9cos(9x)#

Hope this helps!