Apply the quotient rule, which is:
and .
To find :
Rewrite the function to be differentiated:
Apply the quotient rule, which is:
and .
To find :
The derivative of sine is cosine:
To find :
The derivative of cosine is negative sine:
Now plug in to the quotient rule:
To find :
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:
Now plug in to the quotient rule:
Now simplify:
The answer is:
1 / 2 \ tan(x) ---*\1 + tan (x)/ - ------ 4*x 2 4*x
2 tan(x) / 2 \ 1 + tan (x) ------ + \1 + tan (x)/*tan(x) - ----------- 2 x x ------------------------------------------- 2*x
/ 2 \ / 2 \ / 2 \ / 2 \ 3*tan(x) 3*\1 + tan (x)/ 3*\1 + tan (x)/*tan(x) \1 + tan (x)/*\1 + 3*tan (x)/ - -------- + --------------- - ---------------------- 3 2 x x x ----------------------------------------------------------------------------------- 2*x