1 ------------------ 2 (sin(x) + cos(x))
1/((sin(x) + cos(x))^2)
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
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:
The result of the chain rule is:
Now simplify:
The answer is:
-(-2*sin(x) + 2*cos(x)) ------------------------------------ 2 (sin(x) + cos(x))*(sin(x) + cos(x))
/ 2\ | 3*(-cos(x) + sin(x)) | 2*|1 + ---------------------| | 2 | \ (cos(x) + sin(x)) / ----------------------------- 2 (cos(x) + sin(x))
/ 2\ | 3*(-cos(x) + sin(x)) | 8*|2 + ---------------------|*(-cos(x) + sin(x)) | 2 | \ (cos(x) + sin(x)) / ------------------------------------------------ 3 (cos(x) + sin(x))