/ 2 \ x \x + 2*x/*e
d // 2 \ x\ --\\x + 2*x/*e / dx
Apply the product rule:
; to find :
Differentiate term by term:
Apply the power rule: goes to
The derivative of a constant times a function is the constant times the derivative of the function.
Apply the power rule: goes to
So, the result is:
The result is:
; to find :
The derivative of is itself.
The result is:
Now simplify:
The answer is:
x / 2 \ x (2 + 2*x)*e + \x + 2*x/*e
x (6 + 4*x + x*(2 + x))*e
x (12 + 6*x + x*(2 + x))*e