__________ / 2 \/ 2*x - x
/ __________\ d | / 2 | --\\/ 2*x - x / dx
Let .
Apply the power rule: goes to
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 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 is:
The result of the chain rule is:
Now simplify:
The answer is:
1 - x ------------- __________ / 2 \/ 2*x - x
/ 2\ | (-1 + x) | -|1 + ---------| \ x*(2 - x)/ ----------------- ___________ \/ x*(2 - x)
/ 2\ | (-1 + x) | -3*|1 + ---------|*(-1 + x) \ x*(2 - x)/ --------------------------- 3/2 (x*(2 - x))