sin(x) E *cos(3*x)
E^sin(x)*cos(3*x)
Apply the product rule:
; to find :
Let .
The derivative of is itself.
Then, apply the chain rule. Multiply by :
The derivative of sine is cosine:
The result of the chain rule is:
; to find :
Let .
The derivative of cosine is negative sine:
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:
sin(x) sin(x) - 3*e *sin(3*x) + cos(x)*cos(3*x)*e
/ / 2 \ \ sin(x) -\9*cos(3*x) + \- cos (x) + sin(x)/*cos(3*x) + 6*cos(x)*sin(3*x)/*e
/ / 2 \ / 2 \ \ sin(x) \27*sin(3*x) - 27*cos(x)*cos(3*x) + 9*\- cos (x) + sin(x)/*sin(3*x) - \1 - cos (x) + 3*sin(x)/*cos(x)*cos(3*x)/*e