Apply the quotient rule, which is:
and .
To find :
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:
To find :
The derivative of is itself.
Now plug in to the quotient rule:
Now simplify:
The answer is:
-x -x - e *sin(2*x) + 2*cos(2*x)*e
-x -(3*sin(2*x) + 4*cos(2*x))*e
-x (-2*cos(2*x) + 11*sin(2*x))*e