a) f`(x) = (e^x +xlnx -1)` = (e^x)` +(xlnx)` - 1` = e^x +x`(lnx) +x(lnx)` = e^x +lnx +x * 1/x = e^x + lnx+ 1
b) Ecuatia tangentei y-f(x0) = f`(x0)(x-x0)
Dar x0 = 1 => y-f(1) = f`(1)(x-1)
f(1) = e^1 +1ln1 -1 = e -1
f`(1) = e^1+ ln1 + 1 = e +1
=> y-e+1 = (e+1)(x-1)
y-e+1 = ex-e+x-1
y = ex-e+x-1+e-1
y = ex+x-2
y = x(e+1)-2
