3 sin (4*x - 1)
d / 3 \ --\sin (4*x - 1)/ 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:
2 12*sin (4*x - 1)*cos(4*x - 1)
/ 2 2 \ 48*\- sin (-1 + 4*x) + 2*cos (-1 + 4*x)/*sin(-1 + 4*x)
/ 2 2 \ 192*\- 7*sin (-1 + 4*x) + 2*cos (-1 + 4*x)/*cos(-1 + 4*x)