3 sin(x)*log (2*x)
sin(x)*log(2*x)^3
Apply the product rule:
; to find :
The derivative of sine is cosine:
; to find :
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 :
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 of the chain rule is:
The result of the chain rule is:
The result is:
Now simplify:
The answer is:
2 3 3*log (2*x)*sin(x) log (2*x)*cos(x) + ------------------ x
/ 2 3*(-2 + log(2*x))*sin(x) 6*cos(x)*log(2*x)\ |- log (2*x)*sin(x) - ------------------------ + -----------------|*log(2*x) | 2 x | \ x /
2 / 2 \ 3 9*log (2*x)*sin(x) 6*\1 + log (2*x) - 3*log(2*x)/*sin(x) 9*(-2 + log(2*x))*cos(x)*log(2*x) - log (2*x)*cos(x) - ------------------ + ------------------------------------- - --------------------------------- x 3 2 x x