The general equation you're after is [tex]\frac{d}{dx}(x^n)=nx^{n-1}[/tex]MattsAli1108 said:Homework Statement
F(x)= square root of x
what would F'(x)=?
(F prime of x)
Homework Equations
F(x)= 3x^2
F'(x)=6x
F(x)= x^3
F'(x)=3x^2
The Attempt at a Solution
no clue. If the variable is a square root, it wouldn't have an exponent, right?
confused.
The derivative of the square root function, also known as the radical function, is 1/2 times the original function raised to the power of -1/2. In other words, the derivative of √x is 1/(2√x).
To find the derivative of the square root function using the power rule, you can rewrite the function as x^(1/2) and then apply the power rule. This results in 1/2 times x^(1/2 - 1), which simplifies to 1/(2√x).
Yes, the chain rule can be used to find the derivative of the square root function. When using the chain rule, you would first rewrite the function as (x)^(1/2) and then apply the chain rule formula, which results in 1/(2√x).
The quotient rule can also be used to find the derivative of the square root function. To do this, you would first rewrite the function as √x/x, and then apply the quotient rule formula which is (f'(x)g(x) - g'(x)f(x))/[g(x)]^2. This results in 1/(2x^(3/2)).
Yes, there are a few special considerations to keep in mind when finding the derivative of the square root function. These include using the chain rule or quotient rule, being careful with negative values of x, and understanding the domain and range of the square root function. It is also important to remember that the derivative of √x is not defined at x = 0.