f(x)=ln[(1+x)]

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Since the function that has to be differentiated is the result of composition of 2 functions, logarithmic and linear functions, we'll apply the chain rule and we'll differentiate with respect to x.

f'(x) = {ln[(1+x)]}'*(1+x)'

f'(x) = 1/(1+x)

The derivative of the given function is: f'(x)** =**1/(1+x)

The derivative of natural log (ln) is 1 over function 1/x,

f(x)=ln(x) --> f'(x)=1/x

ergo, if f(x)=ln(1+x), then f'(x)=1/(1+x)

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