If #f(x)= tan8 x # and #g(x) = e^(-3x ) #, how do you differentiate #f(g(x)) # using the chain rule?

1 Answer
Jim G.
Jan 20, 2016

<# f'(g(x)) = -24 e^(-3x) . sec^2(8e^(-3x)) #

Explanation:

#f(g(x)) = f( e^(-3x) )= tan(8e^(-3x)) #

using 'chain rule' to differentiate.

# f'(g(x)) = sec^2(8e^(-3x)) d/dx (8e^(-3x)) #

# = sec^2(8e^(-3x)) . 8e^(-3x) d/dx (-3x) #

# = sec^2(8e^(-3x)) .8e^(-3x) . (- 3 ) #

# rArr f'(g(x)) = -24 e^(-3x). sec^2(8e^(-3x)) #

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