10*cos(5*x)*sin(5*x)
(10*cos(5*x))*sin(5*x)
Apply the product rule:
; to find :
The derivative of a constant times a function is the constant times the derivative of the function.
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:
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:
Now simplify:
The answer is:
2 2 - 50*sin (5*x) + 50*cos (5*x)
-1000*cos(5*x)*sin(5*x)