1 1*------------- 2 cos (5*x - 1)
d / 1 \ --|1*-------------| dx| 2 | \ cos (5*x - 1)/
Apply the quotient rule, which is:
and .
To find :
The derivative of the constant is zero.
To find :
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
Let .
The derivative of cosine is negative sine:
Then, apply the chain rule. Multiply by :
Differentiate term by term:
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 derivative of the constant is zero.
The result is:
The result of the chain rule is:
The result of the chain rule is:
Now plug in to the quotient rule:
Now simplify:
The answer is:
10*sin(5*x - 1) -------------------------- 2 cos(5*x - 1)*cos (5*x - 1)
/ 2 \ | 3*sin (-1 + 5*x)| 50*|1 + ----------------| | 2 | \ cos (-1 + 5*x) / ------------------------- 2 cos (-1 + 5*x)
/ 2 \ | 3*sin (-1 + 5*x)| 1000*|2 + ----------------|*sin(-1 + 5*x) | 2 | \ cos (-1 + 5*x) / ----------------------------------------- 3 cos (-1 + 5*x)