___ -x \/ x *e
d / ___ -x\ --\\/ x *e / dx
Apply the quotient rule, which is:
and .
To find :
Apply the power rule: goes to
To find :
The derivative of is itself.
Now plug in to the quotient rule:
Now simplify:
The answer is:
-x e ___ -x ------- - \/ x *e ___ 2*\/ x
/ ___ 1 1 \ -x |\/ x - ----- - ------|*e | ___ 3/2| \ \/ x 4*x /
/ ___ 3 3 3 \ -x |- \/ x + ------- + ------ + ------|*e | ___ 3/2 5/2| \ 2*\/ x 4*x 8*x /