x ------------ 2 x - 3*x + 2
x/(x^2 - 3*x + 2)
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.
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:
Now plug in to the quotient rule:
The answer is:
1 x*(3 - 2*x) ------------ + --------------- 2 2 x - 3*x + 2 / 2 \ \x - 3*x + 2/
/ / 2 \\ | | (-3 + 2*x) || 2*|3 - 2*x + x*|-1 + ------------|| | | 2 || \ \ 2 + x - 3*x// ----------------------------------- 2 / 2 \ \2 + x - 3*x/
/ / 2 \\ | | (-3 + 2*x) || | x*(-3 + 2*x)*|-2 + ------------|| | 2 | 2 || | (-3 + 2*x) \ 2 + x - 3*x/| 6*|-1 + ------------ - --------------------------------| | 2 2 | \ 2 + x - 3*x 2 + x - 3*x / -------------------------------------------------------- 2 / 2 \ \2 + x - 3*x/