2 x + 24 ------- x + 1
/ 2 \ d |x + 24| --|-------| dx\ x + 1 /
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 :
Differentiate term by term:
The derivative of the constant is zero.
Apply the power rule: goes to
The result is:
Now plug in to the quotient rule:
The answer is:
2 x + 24 2*x - -------- + ----- 2 x + 1 (x + 1)
/ 2 \ | 24 + x 2*x | 2*|1 + -------- - -----| | 2 1 + x| \ (1 + x) / ------------------------ 1 + x
/ 2 \ | 24 + x 2*x | 6*|-1 - -------- + -----| | 2 1 + x| \ (1 + x) / ------------------------- 2 (1 + x)