/ ________\ | / 3 | log\\/ x + 4 /
/ / ________\\ d | | / 3 || --\log\\/ x + 4 // dx
Let .
The derivative of is .
Then, apply the chain rule. Multiply by :
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:
The result of the chain rule is:
Now simplify:
The answer is:
2 3*x ---------- / 3 \ 2*\x + 4/
/ 3 \ | 3*x | 3*x*|1 - ----------| | / 3\| \ 2*\4 + x // -------------------- 3 4 + x
/ 3 6 \ | 9*x 9*x | 3*|1 - ------ + ---------| | 3 2| | 4 + x / 3\ | \ \4 + x / / -------------------------- 3 4 + x