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