3 x *cos(5*x)
d / 3 \ --\x *cos(5*x)/ dx
Apply the product rule:
; to find :
Apply the power rule: goes to
; 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:
3 2 - 5*x *sin(5*x) + 3*x *cos(5*x)
/ 2 \ x*\6*cos(5*x) - 30*x*sin(5*x) - 25*x *cos(5*x)/
2 3 6*cos(5*x) - 225*x *cos(5*x) - 90*x*sin(5*x) + 125*x *sin(5*x)