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