Let .
The derivative of is itself.
Then, apply the chain rule. Multiply by :
Let .
The derivative of sine is cosine:
Then, apply the chain rule. Multiply by :
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 of the chain rule is:
The result of the chain rule is:
The answer is:
sin(3*x) 3*cos(3*x)*e
/ 2 \ sin(3*x) 9*\cos (3*x) - sin(3*x)/*e
/ 2 \ sin(3*x) 27*\-1 + cos (3*x) - 3*sin(3*x)/*cos(3*x)*e