differentiate: f(x)=(x^2+1)e^x?

Answer 1

product rule:

d/dx (uv) = u'v + v'u

f'(x) = d/dx (x^2 + 1) e^x + d/dx (e^x) (x^2 + 1)

d/dx (e^x) = e^x

f'(x) = 2x (e^x) + e^x (x^2 + 1)

factor out e^x

f'(x) = e^x (x^2 + 2x + 1)

f'(x) = e^x (x+1)^2 <== answer

Answer 2

f(x)=(x^2+1)e^x
f '(x) = (x^2+1)e^x + 2xe^x = e^x(x^2+2x+1)=e^x(x+1)^2

Answer 3

I'm not sure how these other guys are getting their answers, but the answer is 2xe^x+(x^2+1)e^x.