The discussion revolves around finding the derivatives of various functions and determining the domains of those functions and their derivatives. The scope includes mathematical reasoning and application of differentiation rules such as the power rule and quotient rule.
There is no consensus on the correct derivatives or domains of the functions presented. Participants express differing views on the calculations and interpretations of the functions, leading to some confusion and corrections without a clear resolution.
Participants' understanding of the power rule and the application of the quotient rule appears to vary, leading to uncertainty in derivative calculations. There are also ambiguities in the interpretation of the fourth function, which may affect the discussion of its derivative.
? No, x+ \sqrt{x} is NOT equal to x^{1/2}= \sqrt{x} and NEITHER of those is equal to x^{1/2}. Did you mean that \sqrt{x}= x^{1/2}? And that the derivative is x^{3/2}? That last is not correct, either. Surely, you know what the derivative of x= x1 is 1? And what is the derivative of \sqrt{x}= x^{1/2}?bballj228 said:For the first one i got up to x + √x = x^1/2 = x^3/2
Yes, that is correct!2nd one 1(1-3x) - (-3)(3 + x) all over (1-3x)^2 = 10 / (1 - 3x) ^2
USE the quotient rule of course! What is (x2+ 1)' ? What is (x- 2)'? Do it just like you did number 2.3rd one i know its the quotient rule but not sure where to go with this one
For the fourth i tried the chain rule
√3x + 1 = 3x^1/2 + 1 = 1/2(3x)^1/2
HallsofIvy said:? No, x+ \sqrt{x} is NOT equal to x^{1/2}= \sqrt{x} and NEITHER of those is equal to x^{1/2}. Did you mean that \sqrt{x}= x^{1/2}? And that the derivative is x^{3/2}? That last is not correct, either. Surely, you know what the derivative of x= x1 is 1? And what is the derivative of \sqrt{x}= x^{1/2}?
No, I don't know actually.