___________ / ___ \/ x + \/ x
/ ___________\ d | / ___ | --\\/ x + \/ x / dx
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
Differentiate term by term:
Apply the power rule: goes to
Apply the power rule: goes to
The result is:
The result of the chain rule is:
Now simplify:
The answer is:
1 1 - + ------- 2 ___ 4*\/ x -------------- ___________ / ___ \/ x + \/ x
/ 2\ | / 1 \ | | |2 + -----| | | | ___| | | 2 \ \/ x / | -|---- + ------------| | 3/2 ___ | \x x + \/ x / ----------------------- ___________ / ___ 16*\/ x + \/ x
/ 3 \ | / 1 \ / 1 \ | | |2 + -----| 2*|2 + -----| | | | ___| | ___| | | 4 \ \/ x / \ \/ x / | 3*|---- + ------------ + ----------------| | 5/2 2 3/2 / ___\| |x / ___\ x *\x + \/ x /| \ \x + \/ x / / ------------------------------------------ ___________ / ___ 64*\/ x + \/ x