2 x - 4*x -------- x - 2
/ 2 \ d |x - 4*x| --|--------| dx\ x - 2 /
Apply the quotient rule, which is:
and .
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 :
Differentiate term by term:
The derivative of the constant is zero.
Apply the power rule: goes to
The result is:
Now plug in to the quotient rule:
Now simplify:
The answer is:
2 -4 + 2*x x - 4*x -------- - -------- x - 2 2 (x - 2)
/ x*(-4 + x)\ 2*|-1 + ----------| | 2 | \ (-2 + x) / ------------------- -2 + x
/ x*(-4 + x)\ 6*|1 - ----------| | 2 | \ (-2 + x) / ------------------ 2 (-2 + x)