______________ \/ log(2*x - 5)
sqrt(log(2*x - 5))
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:
The derivative of a constant times a function is the constant times the derivative of the function.
Apply the power rule: goes to
So, the result is:
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 - 5)*\/ log(2*x - 5)
/ 1 \ -|2 + -------------| \ log(-5 + 2*x)/ ----------------------------- 2 _______________ (-5 + 2*x) *\/ log(-5 + 2*x)
3 6 8 + -------------- + ------------- 2 log(-5 + 2*x) log (-5 + 2*x) ---------------------------------- 3 _______________ (-5 + 2*x) *\/ log(-5 + 2*x)