/ 2 \ log\2*x + 3/
d / / 2 \\ --\log\2*x + 3// dx
Let .
The derivative of is .
Then, apply the chain rule. Multiply by :
Differentiate term by term:
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 derivative of the constant is zero.
The result is:
The result of the chain rule is:
Now simplify:
The answer is:
/ 2 \ | 4*x | 4*|1 - --------| | 2| \ 3 + 2*x / ---------------- 2 3 + 2*x
/ 2 \ | 8*x | 16*x*|-3 + --------| | 2| \ 3 + 2*x / -------------------- 2 / 2\ \3 + 2*x /