3 sin (2*x + 1)
d / 3 \ --\sin (2*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 6*sin (2*x + 1)*cos(2*x + 1)
/ 2 2 \ 12*\- sin (1 + 2*x) + 2*cos (1 + 2*x)/*sin(1 + 2*x)
/ 2 2 \ 24*\- 7*sin (1 + 2*x) + 2*cos (1 + 2*x)/*cos(1 + 2*x)