______________ \/ cos(7*x - 1)
d / ______________\ --\\/ cos(7*x - 1) / dx
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 simplify:
The answer is:
-7*sin(7*x - 1) ------------------ ______________ 2*\/ cos(7*x - 1)
/ 2 \ | _______________ sin (-1 + 7*x) | -49*|2*\/ cos(-1 + 7*x) + ----------------| | 3/2 | \ cos (-1 + 7*x)/ -------------------------------------------- 4
/ 2 \ | 3*sin (-1 + 7*x)| -343*|2 + ----------------|*sin(-1 + 7*x) | 2 | \ cos (-1 + 7*x) / ----------------------------------------- _______________ 8*\/ cos(-1 + 7*x)