comment dériver f(x) = (x+1) ln (x+1) -x merci bcp

Bonsoir Dulani357

[tex] f(x) = (x+1)\ln (x+1) -x\\\\ f'(x) = [(x+1)\ln (x+1) -x]'\\\\ f'(x) = [(x+1)\ln (x+1)]' -x'\\\\ f'(x) = (x+1)'\ln (x+1)+(x+1)[\ln(x+1)]' -x'\\\\ f'(x) = 1\times\ln (x+1)+(x+1)\dfrac{1}{x+1} -1\\\\ f'(x) = \ln (x+1)+\dfrac{x+1}{x+1} -1\\\\ f'(x) = \ln (x+1)+1-1[/tex]

[tex]\boxed{f'(x) = \ln (x+1)}[/tex]