Find f′(x) for f(x)=2xln(x+1) . (1 point) Responses f′(x)=2x[ln2 ⋅ ln(x+1)+1x+1] f ' ( x ) = 2 x [ ln 2 · ln ( x + 1 ) + 1 x + 1 ] f′(x)=2x[ln(2x+2)+1x+1] f ' ( x ) = 2 x [ ln ( 2 x + 2 ) + 1 x + 1 ] f′(x)=2x[ln(x+1)+1x+1] f ' ( x ) = 2 x [ ln ( x + 1 ) + 1 x + 1 ] f′(x)=2xln2+1x+1 f ' ( x ) = 2 x ln 2 + 1 x + 1 f′(x)=2xln2x+1
The correct response is:
f′(x)=2ln(x+1)+2x/(x+1)