_____________ / 2 \/ 1 + sin (x)
sqrt(1 + sin(x)^2)
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
Differentiate term by term:
The derivative of the constant is zero.
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
The derivative of sine is cosine:
The result of the chain rule is:
The result is:
The result of the chain rule is:
Now simplify:
The answer is:
cos(x)*sin(x) ---------------- _____________ / 2 \/ 1 + sin (x)
2 2 2 2 cos (x)*sin (x) cos (x) - sin (x) - --------------- 2 1 + sin (x) ----------------------------------- _____________ / 2 \/ 1 + sin (x)
/ 2 2 2 2 \ | 3*cos (x) 3*sin (x) 3*cos (x)*sin (x)| |-4 - ----------- + ----------- + -----------------|*cos(x)*sin(x) | 2 2 2 | | 1 + sin (x) 1 + sin (x) / 2 \ | \ \1 + sin (x)/ / ------------------------------------------------------------------ _____________ / 2 \/ 1 + sin (x)