Question

Calculus Problem

Answer 1

Take the derivative of \[xe^(-x^2/18)\]

Answer 2

xe is raised to the power of negative x squared over 18

Answer 3

its a product and chain rule

Answer 4

\[[xe^{-x^2/18}]' = x'e^{-x^2/18}+x e'^{-x^2/18}\]

Answer 5

so if i needed to solve for x when the derivative of the function was set equal to zero, how would i go about doing that?

Answer 6

\[[xe^{-x^2/18}]' = x'e^{-x^2/18}+x e'^{-x^2/18}\]
\[[xe^{-x^2/18}]' = e^{-x^2/18}+x (-x^2/18)e^{(-x^2/18)-1}(-x^2/18)'\]

\[[xe^{-x^2/18}]' = e^{-x^2/18}+\frac{-x^3e^{(-x^2/18)-1}}{18}\frac{-2x}{18}\]

Answer 7

after the derivative is sorted out, the rest is just algebra to clean it up

Answer 8

as far as seroing it out goes .. good luck :)

Answer 9

thanks!!

Answer 10

http://www.wolframalpha.com/input/?i=x+e^%28-x^2%2F18%29