(1/2 - x)*cos(x) + sin(x)
(1/2 - x)*cos(x) + sin(x)
Differentiate term by term:
Apply the quotient rule, which is:
and .
To find :
Apply the product rule:
; to find :
Differentiate term by term:
The derivative of the constant is zero.
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 is:
; to find :
The derivative of cosine is negative sine:
The result is:
To find :
The derivative of the constant is zero.
Now plug in to the quotient rule:
The derivative of sine is cosine:
The result is:
Now simplify:
The answer is:
-(1/2 - x)*sin(x)
(-1 + 2*x)*cos(x) ----------------- + sin(x) 2
(-1 + 2*x)*sin(x) 2*cos(x) - ----------------- 2