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 :
Differentiate term by term:
The derivative of the constant is zero.
Apply the power rule: goes to
The result is:
Now plug in to the quotient rule:
Now simplify:
The answer is:
2 1 + tan (x) tan(x) ----------- - -------- x + 2 2 (x + 2)
/ 2 \ | tan(x) / 2 \ 1 + tan (x)| 2*|-------- + \1 + tan (x)/*tan(x) - -----------| | 2 2 + x | \(2 + x) / ------------------------------------------------- 2 + x
/ / 2 \ / 2 \ \ |/ 2 \ / 2 \ 3*tan(x) 3*\1 + tan (x)/ 3*\1 + tan (x)/*tan(x)| 2*|\1 + tan (x)/*\1 + 3*tan (x)/ - -------- + --------------- - ----------------------| | 3 2 2 + x | \ (2 + x) (2 + x) / --------------------------------------------------------------------------------------- 2 + x