___ 1 + x - 4*\/ x --------------- x
Apply the quotient rule, which is:
and .
To find :
Differentiate term by term:
The derivative of the constant is zero.
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:
To find :
Apply the power rule: goes to
Now plug in to the quotient rule:
Now simplify:
The answer is:
2 1 - ----- ___ ___ \/ x 1 + x - 4*\/ x --------- - --------------- x 2 x
/ 2 \ 2*|1 - -----| | ___| / ___\ 1 \ \/ x / 2*\1 + x - 4*\/ x / ---- - ------------- + ------------------- 5/2 2 3 x x x
/ / 2 \\ | 2*|1 - -----|| | / ___\ | ___|| | 3 2*\1 + x - 4*\/ x / \ \/ x /| 3*|- ------ - ------------------- + -------------| | 7/2 4 3 | \ 2*x x x /