How to differentiate #ln(e^(3x) +2)#?
1 Answer
Jun 24, 2018
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)#