Stanc said:Homework Statement
If p(x) = (2x+8) / (√x) Prove that p'(x) is (x√x - 4√x)/x
The Attempt at a Solution
I keep getting stumped, I cannot simplify it down
Dick said:Well, what's your answer? Show your work. I think the given answer is wrong.
SteamKing said:You can try simplifying it algebraically. Remember, you are trying to match a given answer.
Stanc said:What do you mean by simplifying it algebraically?? Can you give me a start?
A derivative is a mathematical concept that represents the rate of change of a function at a specific point. It measures how much a function is changing at that point, which can be interpreted as the slope of the function's graph at that point.
In order to prove the derivative of p(x), you will need to use the definition of the derivative, which involves taking the limit of the difference quotient as the change in x approaches 0. By evaluating this limit, you can determine the exact value of the derivative at a specific point.
Yes, the power rule is one of the basic rules of differentiation and can be used to find the derivative of a polynomial function. It states that the derivative of x^n is n times x^(n-1), where n is any real number.
The chain rule is a rule of differentiation that allows us to find the derivative of composite functions. In the context of finding the derivative of p(x), the chain rule would be used when p(x) is composed of multiple functions, such as p(x) = sin(x^2). In this case, you would use the chain rule to find the derivative of the inner function (x^2) and then multiply it by the derivative of the outer function (sin).
Yes, the derivative of p(x) can be undefined at certain points where the function is not differentiable. This can happen when the function has a sharp corner or a vertical tangent at that point, meaning the slope of the function is undefined.