-x --- 4 E *sin(2*x)
E^(-x/4)*sin(2*x)
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 :
Let .
The derivative of is itself.
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:
Now plug in to the quotient rule:
Now simplify:
The answer is:
-x -x --- --- 4 4 e *sin(2*x) 2*cos(2*x)*e - ------------- 4
-x --- /63*sin(2*x) \ 4 -|----------- + cos(2*x)|*e \ 16 /