Let .
The derivative of is .
Then, apply the chain rule. Multiply by :
Apply the product rule:
; to find :
Apply the power rule: goes to
; to find :
The derivative of is itself.
The result is:
The result of the chain rule is:
Now simplify:
The answer is:
/ 2 x x\ -x \x *e + 2*x*e /*e -------------------- 2 x
2 2 + x + 4*x 2*(2 + x) -2 - x + ------------ - --------- x x --------------------------------- x
2 / 2 \ / 2 \ 6 + x + 6*x 4*\2 + x + 4*x/ 2*\2 + x + 4*x/ 4*(2 + x) 6*(2 + x) 2 + x + ------------ - ---------------- - ---------------- + --------- + --------- x 2 x x 2 x x ---------------------------------------------------------------------------------- x