2 2*x *cos(2*x) + 2*x*sin(2*x)
(2*x^2)*cos(2*x) + (2*x)*sin(2*x)
Differentiate term by term:
Apply the product rule:
; to find :
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:
; 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:
Apply the product rule:
; to find :
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:
; 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:
The result is:
The answer is:
2 2*sin(2*x) - 4*x *sin(2*x) + 8*x*cos(2*x)
/ 2 \ 4*\3*cos(2*x) - 6*x*sin(2*x) - 2*x *cos(2*x)/