Can't we just use rules of exponent first before doing any quotient rule? y = [(x+1)/(x+1)²]^½ since we are dividing quantities of the same base, we get y = [(x+1)^(1-2)]^½ y = [(x+1)^-1]^½ Then power of a power rule. We multiply the exponents y = (x+1)^(-1/2) Chain rule is easier applied on that. Why didn't we do that, just curious. Is there a rule or a restriction in the domain that won't allow us to do that?
Can't we just use rules of exponent first before doing any quotient rule?
y = [(x+1)/(x+1)²]^½
since we are dividing quantities of the same base, we get
y = [(x+1)^(1-2)]^½
y = [(x+1)^-1]^½
Then power of a power rule. We multiply the exponents
y = (x+1)^(-1/2)
Chain rule is easier applied on that. Why didn't we do that, just curious. Is there a rule or a restriction in the domain that won't allow us to do that?
Yeah, you are kinda correct, I goes the longway because of what I want to teach the class.