x*(x - 2) ---------- 2 2*(x - 1)
d /x*(x - 2) \ --|----------| dx| 2| \2*(x - 1) /
Apply the quotient rule, which is:
and .
To find :
Apply the product rule:
; to find :
Apply the power rule: goes to
; to find :
Differentiate term by term:
The derivative of the constant is zero.
Apply the power rule: goes to
The result is:
The result is:
To find :
The derivative of a constant times a function is the constant times the derivative of the function.
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
Differentiate term by term:
The derivative of the constant is zero.
Apply the power rule: goes to
The result is:
The result of the chain rule is:
So, the result is:
Now plug in to the quotient rule:
Now simplify:
The answer is:
1 1 x*(4 - 4*x)*(x - 2) x*---------- + ----------*(x - 2) + ------------------- 2 2 4 2*(x - 1) 2*(x - 1) 4*(x - 1)
2*x 2*(-2 + x) 3*x*(-2 + x) 1 - ------ - ---------- + ------------ -1 + x -1 + x 2 (-1 + x) -------------------------------------- 2 (-1 + x)
/ 3*x 3*(-2 + x) 4*x*(-2 + x)\ 3*|-2 + ------ + ---------- - ------------| | -1 + x -1 + x 2 | \ (-1 + x) / ------------------------------------------- 3 (-1 + x)