2 sin (2*x - 3)
d / 2 \ --\sin (2*x - 3)/ dx
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 :
Differentiate term by term:
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:
The result of the chain rule is:
Now simplify:
The answer is:
4*cos(2*x - 3)*sin(2*x - 3)
/ 2 2 \ 8*\cos (-3 + 2*x) - sin (-3 + 2*x)/
-64*cos(-3 + 2*x)*sin(-3 + 2*x)