3 ______________ \/ log(5 - 2*x)
log(5 - 2*x)^(1/3)
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:
The derivative of the constant is zero.
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 result is:
The result of the chain rule is:
The result of the chain rule is:
Now simplify:
The answer is:
-2 --------------------------- 2/3 3*(5 - 2*x)*log (5 - 2*x)
/ 2 \ -4*|3 + ------------| \ log(5 - 2*x)/ ----------------------------- 2 2/3 9*(-5 + 2*x) *log (5 - 2*x)
/ 5 9 \ 16*|9 + ------------- + ------------| | 2 log(5 - 2*x)| \ log (5 - 2*x) / ------------------------------------- 3 2/3 27*(-5 + 2*x) *log (5 - 2*x)