4/ _________\ log \\/ 3*x + 5 /
log(sqrt(3*x + 5))^4
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:
3/ _________\ 6*log \\/ 3*x + 5 / ------------------- 3*x + 5
2/ _________\ / / _________\\ 9*log \\/ 5 + 3*x /*\3 - 2*log\\/ 5 + 3*x // -------------------------------------------- 2 (5 + 3*x)
/ / _________\ 2/ _________\\ / _________\ 27*\3 - 9*log\\/ 5 + 3*x / + 4*log \\/ 5 + 3*x //*log\\/ 5 + 3*x / ------------------------------------------------------------------ 3 (5 + 3*x)