2*x e *sin(2*x)
d / 2*x \ --\e *sin(2*x)/ dx
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:
2*x 2*x 2*cos(2*x)*e + 2*e *sin(2*x)
2*x 16*(-sin(2*x) + cos(2*x))*e