3*x - 1 ---------- 2 (2*x + 1)
(3*x - 1)/(2*x + 1)^2
Apply the quotient rule, which is:
and .
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:
To find :
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
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:
The result of the chain rule is:
Now plug in to the quotient rule:
Now simplify:
The answer is:
3 (-4 - 8*x)*(3*x - 1) ---------- + -------------------- 2 4 (2*x + 1) (2*x + 1)
/ -1 + 3*x\ 24*|-1 + --------| \ 1 + 2*x / ------------------ 3 (1 + 2*x)
/ 8*(-1 + 3*x)\ 24*|9 - ------------| \ 1 + 2*x / --------------------- 4 (1 + 2*x)