I've got a question asking me to "differentiate $x^3 e^{-2x}$ using the product rule.
So I differentiate using it $(u v)'=u'v+uv'$ and get
- $u: x^3$
- $u':3x^2$
- $v: e^{-2x}$
- $v':-2e^{-2x}$
Adding them together: $x^3$ $-2e^{-2x}$ + $3x^2$ $e^{-2x}$
The answer I'm 'supposed' to get, however, is $dy/dx= e^{-2x}(3x^2-2x^3)$
What's the logic from going to the final answer, from what I got before? It looked like simple factorization at first, but the logic behind it isn't too clear to me.
Any insights?
Thanks!