determining if the derivative rules apply.

Question

The function (x+3)^(1/2) power was given and I have to determine if the power, constant, and sum difference rule applies. I said no to the power rule because it isn't just x being raised to the power, I sad no to the constant rule since no constant is in front or x, and I said no to the sum and difference rule since it would have two variables to indicate two functions right? I'm a little unsure about the power and sum difference rule being applicable, so If you could please explain it to me. I've been thinking about this question for a long time and I still cant sort it out.

Answer 1

The power rule does apply in addition to the chain rule.

 

(x + 3)^(1/2)  The chain rule is simply using the power rule on the exponent and then taking the derivative inside the parentheses. The two derivatives are multiplied together.

 

(1/2)(x + 3)^(-1/2) * 1     Derivative of x is 1

 

(1/2)(x + 3)^(-1/2)

 

Can be written as 1/[2((x + 3)^(1/2)] in case instructor wants answers in positive exponents.