Differentiate term by term:
Apply the product rule:
; to find :
Apply the power rule: goes to
; to find :
Rewrite the function to be differentiated:
Apply the quotient rule, which is:
and .
To find :
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:
To find :
Let .
The derivative of cosine is negative sine:
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:
Now plug in to the quotient rule:
The result is:
The result is:
Now simplify:
The answer is:
/ 2 \ x x*\3 + 3*tan (3*x)/ + 2 *log(2) + tan(3*x)
2 x 2 / 2 \ 6 + 6*tan (3*x) + 2 *log (2) + 18*x*\1 + tan (3*x)/*tan(3*x)
2 x 3 / 2 \ / 2 \ 2 / 2 \ 2 *log (2) + 54*x*\1 + tan (3*x)/ + 54*\1 + tan (3*x)/*tan(3*x) + 108*x*tan (3*x)*\1 + tan (3*x)/