/ 2\ 2*x \1 - x /*e
d // 2\ 2*x\ --\\1 - x /*e / dx
Apply the product rule:
; to find :
Differentiate term by term:
The derivative of the constant is zero.
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 :
Let .
The derivative of is itself.
Then, apply the chain rule. Multiply by :
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 of the chain rule is:
The result is:
Now simplify:
The answer is:
2*x / 2\ 2*x - 2*x*e + 2*\1 - x /*e
/ 2 \ 2*x -2*\-1 + 2*x + 4*x/*e
/ 2 \ 2*x -4*\1 + 2*x + 6*x/*e