How to differentiate ln(e^(3x) +2)ln(e3x+2)?

1 Answer
Jim G.
Jun 24, 2018

(3e^(3x))/(e^(3x)+2)3e3xe3x+2

Explanation:

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

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