Question

f(x)=(x-1) e la puterea x
aratati ca f derivat (x) =e la puterea x +f(x)

Answer 1

$f'(x)=((x-1)(e^{x}))' = (x-1)' * e^{x} + (x-1) * (e^x)' =$$1 * e^x + (x-1) * (e^x * ln(e)) = e^x + (x-1)*e^x = e^x + f(x)$