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

1 Answer
Jim G.
Apr 1, 2016

#6sec^2(3x)tan(3x) #

Explanation:

differentiating using the #color(blue)" chain rule " #

#d/dx [f(g(x) ] = f'(g(x).g'(x) #

and the standard derivative : #d/dx(secx) = secx.tanx #
#" ----------------------------------------------------------"#

f(g(x) = # [sec(3x)]^2 rArr f'(g(x)) = 2sec(3x)#

and g(x) =#sec(3x) rArr g'(x) = sec(3x).tan(3x). d/dx(3x) #

# = 3sec(3x).tan(3x)#
#" ------------------------------------------------------"#

#rArr f'(x) = 2sec(3x). 3sec(3x).tan(3x)#

# = 6 sec^2(3x).tan(3x)#

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