1 x - 1*------- 2 cos (x)
d / 1 \ --|x - 1*-------| dx| 2 | \ cos (x)/
Differentiate term by term:
Apply the power rule: goes to
The derivative of a constant times a function is the constant times the derivative of the function.
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
The derivative of cosine is negative sine:
The result of the chain rule is:
The result of the chain rule is:
So, the result is:
The result is:
The answer is:
2*sin(x) 1 - -------- 3 cos (x)
/ 2 \ | 3*sin (x)| -2*|1 + ---------| | 2 | \ cos (x) / ------------------ 2 cos (x)
/ 2 \ | 3*sin (x)| -8*|2 + ---------|*sin(x) | 2 | \ cos (x) / ------------------------- 3 cos (x)