_________ \/ 2*x + 5
d / _________\ --\\/ 2*x + 5 / dx
Let .
Apply the power rule: goes to
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:
-1 ------------ 3/2 (5 + 2*x)
3 ------------ 5/2 (5 + 2*x)