If #f(x)= sin6 x # and #g(x) = e^(3+2x ) #, how do you differentiate #f(g(x)) # using the chain rule?

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Answer 1 · 2016-01-06T04:42:05

Step by step explanation is given below.

Chain rule #(f(g(x)))' = f'(g(x))**g'(x)#

#f(x) = sin(6x)#
Differentiating with respect to x using chain rule

#f'(x) = cos(6x)d/dx(6x)#
#f'(x) = 6cos(6x)#

#g(x) = e^(3+2x)#
Differentiating with respect to x using chain rule
#g'(x) = e^(3+2x)d/dx(3+2x)#
#g'(x)=e^(3+2x)(2)#
#g'(x)=2e^(3+2x)#

We are to find derivative of #f(g(x))#

#f'(g(x)) = 6cos(6e^(3+2x))#

Using the chain rule
#(f(g(x)))' = f'(g(x))**g'(x)#

#(f(g(x)))' = 6cos(6e^(3+2x))(2e^(3+2x))#

#(f(g(x)))' = 12e^(3+2x)cos(6e^(3+2x))# Answer