3 2 log (x)*(2*x + 3)
log(x)^3*(2*x + 3)^2
Apply the product rule:
; to find :
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
The derivative of is .
The result of the chain rule is:
; to find :
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 is:
Now simplify:
The answer is:
2 2 3 3*(2*x + 3) *log (x) log (x)*(12 + 8*x) + -------------------- x
/ 2 \ | 2 3*(3 + 2*x) *(-2 + log(x)) 24*(3 + 2*x)*log(x)| |8*log (x) - -------------------------- + -------------------|*log(x) | 2 x | \ x /
/ 2 / 2 \ \ | 2 (3 + 2*x) *\1 + log (x) - 3*log(x)/ 6*(-2 + log(x))*(3 + 2*x)*log(x)| 6*|12*log (x) + ----------------------------------- - --------------------------------| | 2 x | \ x / --------------------------------------------------------------------------------------- x