How do you differentiate # f(x)=(ln(6x+8))^2# using the chain rule.?

1 Answer
Gió
Jun 3, 2016

I found: #f'(x)=6/(3x+4)ln(6x+8)#

Explanation:

First derive the #()^2# as it is then multiply by the derivative of the #ln# (red) and finally multply by the derivative of the argument of the #ln# (blue):
#f'(x)=2(ln(6x+8))^(2-1)*color(red)(1/(6x+8))*color(blue)(6)=#
#=12/(6x+8)ln(6x+8)=12/(2(3x+4))ln(6x+8)=#
#=6/(3x+4)ln(6x+8)#

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