________ / 3 \/ x + 2
/ ________\ d | / 3 | --\\/ x + 2 / dx
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
Differentiate term by term:
Apply the power rule: goes to
The derivative of the constant is zero.
The result is:
The result of the chain rule is:
Now simplify:
The answer is:
2 3*x ------------- ________ / 3 2*\/ x + 2
/ 3 \ | 3*x | 3*x*|1 - ----------| | / 3\| \ 4*\2 + x // -------------------- ________ / 3 \/ 2 + x
/ 3 6 \ | 9*x 27*x | 3*|1 - ---------- + -----------| | / 3\ 2| | 2*\2 + x / / 3\ | \ 8*\2 + x / / -------------------------------- ________ / 3 \/ 2 + x