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:
2 x + 5 2*x - -------- + ----- 2 x - 3 (x - 3)
/ 2 \ | 5 + x 2*x | 2*|1 + --------- - ------| | 2 -3 + x| \ (-3 + x) / -------------------------- -3 + x
/ 2 \ | 5 + x 2*x | 6*|-1 - --------- + ------| | 2 -3 + x| \ (-3 + x) / --------------------------- 2 (-3 + x)