x*(-2) E *sin(3*x)
E^(x*(-2))*sin(3*x)
Apply the product rule:
; 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:
; 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:
The result is:
Now simplify:
The answer is:
x*(-2) x*(-2) - 2*e *sin(3*x) + 3*cos(3*x)*e
-2*x (-12*cos(3*x) - 5*sin(3*x))*e