5/ _________\ log \\/ 3*x + 5 /
log(sqrt(3*x + 5))^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 :
Let .
Apply the power rule: goes to
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:
The result of the chain rule is:
Now simplify:
The answer is:
4/ _________\ 15*log \\/ 3*x + 5 / -------------------- 2*(3*x + 5)
/ / _________\\ 3/ _________\ | log\\/ 5 + 3*x /| 45*log \\/ 5 + 3*x /*|1 - ----------------| \ 2 / ------------------------------------------- 2 (5 + 3*x)
2/ _________\ /3 2/ _________\ / _________\\ 135*log \\/ 5 + 3*x /*|- + log \\/ 5 + 3*x / - 3*log\\/ 5 + 3*x /| \2 / ------------------------------------------------------------------ 3 (5 + 3*x)