1 ----------- _______ 3*\/ x + 1
1/(3*sqrt(x + 1))
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
The derivative of a constant times a function is the constant times the derivative of the function.
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
Differentiate term by term:
Apply the power rule: goes to
The derivative of the constant is zero.
The result is:
The result of the chain rule is:
So, the result is:
The result of the chain rule is:
Now simplify:
The answer is:
1 - ----------- _______ 3*\/ x + 1 -------------- 2*(x + 1)
1 ------------ 5/2 4*(1 + x)
-5 ------------ 7/2 8*(1 + x)