3/t\ sin |-| \3/
d / 3/t\\ --|sin |-|| dt\ \3//
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:
Now simplify:
The answer is:
2/t\ /t\ sin |-|*cos|-| \3/ \3/
/ 2/t\ 2/t\\ /t\ |- sin |-| + 2*cos |-||*sin|-| \ \3/ \3// \3/ ------------------------------ 3
/ 2/t\ 2/t\\ /t\ |- 7*sin |-| + 2*cos |-||*cos|-| \ \3/ \3// \3/ -------------------------------- 9