Apply the quotient rule, which is:
and .
To find :
Differentiate term by term:
The derivative of the constant is zero.
Apply the power rule: goes to
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:
The answer is:
1 2*x*(x + 2) ------ - ----------- 2 2 x - 9 / 2 \ \x - 9/
/ / 2 \ \ | | 4*x | | 2*|-2*x + |-1 + -------|*(2 + x)| | | 2| | \ \ -9 + x / / --------------------------------- 2 / 2\ \-9 + x /
/ / 2 \ \ | | 2*x | | | 4*x*|-1 + -------|*(2 + x)| | 2 | 2| | | 4*x \ -9 + x / | 6*|-1 + ------- - --------------------------| | 2 2 | \ -9 + x -9 + x / --------------------------------------------- 2 / 2\ \-9 + x /