sin(x) ---------- 1 + cos(x)
sin(x)/(1 + cos(x))
Apply the quotient rule, which is:
and .
To find :
The derivative of sine is cosine:
To find :
Differentiate term by term:
The derivative of the constant is zero.
The derivative of cosine is negative sine:
The result is:
Now plug in to the quotient rule:
Now simplify:
The answer is:
2 cos(x) sin (x) ---------- + ------------- 1 + cos(x) 2 (1 + cos(x))
/ 2 \ | 2*sin (x) | | ---------- + cos(x) | | 1 + cos(x) 2*cos(x) | |-1 + ------------------- + ----------|*sin(x) \ 1 + cos(x) 1 + cos(x)/ ---------------------------------------------- 1 + cos(x)
/ 2 \ 2 | 6*cos(x) 6*sin (x) | / 2 \ sin (x)*|-1 + ---------- + -------------| |2*sin (x) | 2 | 1 + cos(x) 2| 3*|---------- + cos(x)|*cos(x) 3*sin (x) \ (1 + cos(x)) / \1 + cos(x) / -cos(x) - ---------- + ----------------------------------------- + ------------------------------ 1 + cos(x) 1 + cos(x) 1 + cos(x) ------------------------------------------------------------------------------------------------- 1 + cos(x)