1 1*----------- ________ / 2 \/ x + 4
d / 1 \ --|1*-----------| dx| ________| | / 2 | \ \/ x + 4 /
Apply the quotient rule, which is:
and .
To find :
The derivative of the constant is zero.
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.
Apply the power rule: goes to
The result is:
The result of the chain rule is:
Now plug in to the quotient rule:
The answer is:
-x -------------------- ________ / 2 \ / 2 \x + 4/*\/ x + 4
2 3*x -1 + ------ 2 4 + x ----------- 3/2 / 2\ \4 + x /
/ 2 \ | 5*x | -3*x*|-3 + ------| | 2| \ 4 + x / ------------------ 5/2 / 2\ \4 + x /