1 --------------- sin(x) + cos(x)
1/(sin(x) + cos(x))
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
Differentiate term by term:
The derivative of sine is cosine:
The derivative of cosine is negative sine:
The result is:
The result of the chain rule is:
Now simplify:
The answer is:
-cos(x) + sin(x) ------------------ 2 (sin(x) + cos(x))
2 2*(-cos(x) + sin(x)) 1 + --------------------- 2 (cos(x) + sin(x)) ------------------------- cos(x) + sin(x)
/ 2\ | 6*(-cos(x) + sin(x)) | |5 + ---------------------|*(-cos(x) + sin(x)) | 2 | \ (cos(x) + sin(x)) / ---------------------------------------------- 2 (cos(x) + sin(x))