____________ \/ log(x - 3)
sqrt(log(x - 3))
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
Let .
The derivative of is .
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:
1 ------------------------ ____________ 2*(x - 3)*\/ log(x - 3)
/ 1 \ -|2 + -----------| \ log(-3 + x)/ --------------------------- 2 _____________ 4*(-3 + x) *\/ log(-3 + x)
3 3 1 + ------------- + -------------- 4*log(-3 + x) 2 8*log (-3 + x) ---------------------------------- 3 _____________ (-3 + x) *\/ log(-3 + x)