Question

Am nevoie de ex 1(a și b) va rog

Answer 1

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