1 --------- 2 sin (2*x)
1/(sin(2*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 :
Let .
The derivative of sine is cosine:
Then, apply the chain rule. Multiply by :
The derivative of a constant times a function is the constant times the derivative of the function.
Apply the power rule: goes to
So, the result is:
The result of the chain rule is:
The result of the chain rule is:
The result of the chain rule is:
The answer is:
-4*cos(2*x) ------------------ 2 sin(2*x)*sin (2*x)
/ 2 \ | 3*cos (2*x)| 8*|1 + -----------| | 2 | \ sin (2*x) / ------------------- 2 sin (2*x)
/ 2 \ | 3*cos (2*x)| -64*|2 + -----------|*cos(2*x) | 2 | \ sin (2*x) / ------------------------------ 3 sin (2*x)