log(x) ------ + 1 x + 2
log(x)/(x + 2) + 1
Differentiate term by term:
Apply the quotient rule, which is:
and .
To find :
The derivative of 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 derivative of the constant is zero.
The result is:
Now simplify:
The answer is:
1 log(x) --------- - -------- x*(x + 2) 2 (x + 2)
1 2 2*log(x) - -- - --------- + -------- 2 x*(2 + x) 2 x (2 + x) --------------------------- 2 + x
2 6*log(x) 3 6 -- - -------- + ---------- + ---------- 3 3 2 2 x (2 + x) x *(2 + x) x*(2 + x) --------------------------------------- 2 + x