x + 4 ----- ___ \/ x
d /x + 4\ --|-----| dx| ___| \\/ 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 result is:
To find :
Apply the power rule: goes to
Now plug in to the quotient rule:
Now simplify:
The answer is:
1 x + 4 ----- - ------ ___ 3/2 \/ x 2*x
3*(4 + x) -1 + --------- 4*x -------------- 3/2 x
/ 5*(4 + x)\ 3*|6 - ---------| \ x / ----------------- 5/2 8*x