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 15*sin (5*x + 3)*cos(5*x + 3)
/ 2 2 \ 75*\- sin (3 + 5*x) + 2*cos (3 + 5*x)/*sin(3 + 5*x)
/ 2 2 \ 375*\- 7*sin (3 + 5*x) + 2*cos (3 + 5*x)/*cos(3 + 5*x)