calculus: if f(x)= ln(x+4+e^-3x), then f ' (0) is?

please explain/show all work

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f'(x) = (1â3e^â(3x))/(e^â(3x)+x+4)

is the derivative of that function

it's chain rule, get the derivative of ln(x+4+e^-3x) first, which is just 1/(x+4+e^-3x) then multiply it by the derivative of x + 4 + e^-3x which is just 1 - 3e^-3x

plug 0 in for all the x values and your solution is -2/5

**I think this is the correct answer**