log(sin(3*x))
d --(log(sin(3*x))) dx
Let .
The derivative of is .
Then, apply the chain rule. Multiply by :
Let .
The derivative of sine is cosine:
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:
Now simplify:
The answer is:
3*cos(3*x) ---------- sin(3*x)
/ 2 \ | cos (3*x)| -9*|1 + ---------| | 2 | \ sin (3*x)/
/ 2 \ | cos (3*x)| 54*|1 + ---------|*cos(3*x) | 2 | \ sin (3*x)/ --------------------------- sin(3*x)