Apply the quotient rule, which is:
and .
To find :
Apply the power rule: goes to
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:
Now plug in to the quotient rule:
Now simplify:
The answer is:
4 2 2*x 3*x --------- + ------ 2 2 / 2\ 4 - x \4 - x /
/ / 2 \\ | 2 | 4*x || | x *|-1 + -------|| | 2 | 2|| | 6*x \ -4 + x /| 2*x*|-3 + ------- - -----------------| | 2 2 | \ -4 + x -4 + x / -------------------------------------- 2 -4 + x
/ / 2 \ / 2 \\ | 2 | 4*x | 4 | 2*x || | 3*x *|-1 + -------| 4*x *|-1 + -------|| | 2 | 2| | 2|| | 6*x \ -4 + x / \ -4 + x /| 6*|-1 + ------- - ------------------- + -------------------| | 2 2 2 | | -4 + x -4 + x / 2\ | \ \-4 + x / / ------------------------------------------------------------ 2 -4 + x