? No, [itex]x+ \sqrt{x}[/itex] is NOT equal to [itex]x^{1/2}= \sqrt{x}[/itex] and NEITHER of those is equal to [itex]x^{1/2}[/itex]. Did you mean that [itex]\sqrt{x}= x^{1/2}[/itex]? And that the derivative is [itex]x^{3/2}[/itex]? That last is not correct, either. Surely, you know what the derivative of x= x1 is 1? And what is the derivative of [itex]\sqrt{x}= x^{1/2}[/itex]?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, [itex]x+ \sqrt{x}[/itex] is NOT equal to [itex]x^{1/2}= \sqrt{x}[/itex] and NEITHER of those is equal to [itex]x^{1/2}[/itex]. Did you mean that [itex]\sqrt{x}= x^{1/2}[/itex]? And that the derivative is [itex]x^{3/2}[/itex]? That last is not correct, either. Surely, you know what the derivative of x= x1 is 1? And what is the derivative of [itex]\sqrt{x}= x^{1/2}[/itex]?
No, I don't know actually.
The domain of a function is the set of all possible input values or independent variables for which the function is defined. In other words, it is the set of all values that can be plugged into the function to produce a valid output.
The domain of a function is typically represented using interval notation or set notation. For example, if the function is defined for all real numbers, the domain can be represented as (-∞, ∞) or {x|x ∈ ℝ}.
Yes, the domain of a function can be restricted based on the context or purpose of the function. For example, the domain of a square root function can be restricted to non-negative real numbers to ensure a real output.
The domain of the derivative of a function is the same as the domain of the original function. Both the function and its derivative are defined for the same set of input values.
The domain of the derivative is a subset of the domain of the function. This means that the derivative is only defined for a subset of the input values that the function is defined for. However, the domain of the derivative can also be restricted if the function has any discontinuities or undefined points within its domain.