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 :
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.
Apply the power rule: goes to
So, the result is:
The result is:
The result of the chain rule is:
So, the result is:
The result is:
Now simplify:
The answer is:
-1/2 + x 1 - ----------- ________ / 2 \/ x - x
2 (-1 + 2*x) -1 + ------------ 4*x*(-1 + x) ----------------- ____________ \/ x*(-1 + x)
/ 2\ | (-1 + 2*x) | 3*(-1 + 2*x)*|4 - -----------| \ x*(-1 + x)/ ------------------------------ 3/2 8*(x*(-1 + x))