How to differentiate #ln(e^(3x) +2)#?

1 Answer
Jim G.
Jun 24, 2018

#(3e^(3x))/(e^(3x)+2)#

Explanation:

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

#"given "y=f(g(x))" then"#

#dy/dx=f'(g(x))xxg'(x)larrcolor(blue)"chain rule"#

#"noting that "d/dx(ln(f(x)))=1/(f(x))xxf'(x)#

#d/dx(ln(e^(3x)+2))#

#=1/(e^(3x)+2)xxd/dx(e^(3x)+2)#

#=1/(e^(3x)+2)xxe^(3x)xxd/dx(3x)#

#=(3e^(3x))/(e^(3x)+2)#

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